Sequence

Problem 1

Find the limit of the sequence $a_{n}=\sqrt{n^{2}+3 n}-n$ . Options: A) 3 B) 2 C) $1 / 2$ D) $3 / 2$ E) 0 F) 1 G) $\infty$ H) does not exist.

See Solution

Problem 2

Ibrahim dan Zahra datang ke mesjid setiap 4 dan 6 hari. Apakah mereka bersama lagi pada 12, 14, dan 26 Juli 2022?

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Problem 3

Ibrahim dan Zahra datang bersama pada 2 Juli 2022. Kapan mereka akan bersama lagi? Tandai dengan $\sqrt{ }$ pilihanmu!
1. 12 Juli 2022
2. 14 Juli 2022
3. 26 Juli 2022
4. 7 Agustus 2022

See Solution

Problem 4

Digite o número que falta na sequência: $1, 2, \square, 8, 16, 32$ .

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Problem 5

Buat kesimpulan umum secara induksi untuk urutan nombor $-\frac{1}{2}, \frac{3}{2}, \frac{25}{6}, \ldots$ mengikut pola yang diberikan.

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Problem 6

Calculate $12 / 20$ and find the missing number in the sequence: 100, 93, 84, 73.

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Problem 7

Find the next number in the sequence: $6, 3, 12, 9, 36, 33$ .

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Problem 8

Find the next number in the sequence: 7, 11, 16, 22, 29, ?

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Problem 9

Identify which sequence is arithmetic and which is geometric: Sequence #1: $5, 15, 45, 135, 405$ ; Sequence #2: $5, 15, 25, 35, 45$ .

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Problem 10

Compare the $15^{\text {th }}$ term of the arithmetic sequence $150,650,1150,1650,...$ and geometric sequence $4,12,36,108,...$ . Show your work.

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Problem 11

Compare the $15^{\text{th}}$ term of the sequences: Arithmetic: $150, 650, 1150, \ldots$ and Geometric: $4, 12, 36, \ldots$ .

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Problem 12

Find the 6th and 7th terms of the sequence $7n-5$ ; also, find the sum of the 100th and 200th terms. Is 99 a term?

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Problem 13

Find the 10th term of the sequence $n^2$ and the $n$ where $2n^2 - 16 = n^2$ .

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Problem 14

En la secuencia, cada número es la suma de los dos anteriores. ¿Cuál es el valor de $x$ en la fila? 10, 16, 28, 26, 149.

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Problem 15

En una secuencia, cada número se forma sumando los dos de arriba. ¿Qué valor tiene $x$ si 26 = 10 + 16?

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Problem 16

Arithmetic Progression Questions:
1. Is this an AP? $2, -2, -6, -10, \ldots$
2. Next two terms of $3, \frac{7}{2}, 4, \frac{9}{2}, \ldots$ ?
3. Common difference of $2+\sqrt{5}, 2+3\sqrt{5}, 2+5\sqrt{5}, \ldots$ ?
4. Sum of first 500 natural numbers?

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Problem 17

Find the missing numbers in the sequence 81, 82, 84, 86 on a number line from 81 to 100, increasing by 2 each time.

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Problem 18

How much will Cardo save on the 9th day if he starts with \$75 and doubles his savings daily?

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Problem 19

Identify the pattern starting with 5 that follows "subtract 2, then multiply by 3": a. $5,7,21,69$ b. $5,2,4,1,2$ c. $5,15,13,39,37$ d. $5,3,9,7,21,19$

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Problem 20

Cari sebutan ke- $n$ , $T_{n}$ , dari pola: $5=3+2(1)$ , $9=3+3(2)$ , $15=3+4(3)$ .

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Problem 21

Find the common ratio $r$ of the geometric sequence 7, 189, $y$ , 1701. Then, determine the smallest integer $n$ for which the $n$ -th term exceeds 10,000.

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Problem 22

Execute $n$ processes with given times. When executing time[i], reduce all equal times to $\lceil \text{time}[i]/2 \rceil$ . Find total execution time.

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Problem 23

Find the next number in the sequence: $3,4,1,8,5,2,9,10,1, ?$ a. 13 b. 6 c. 5 d. 7

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Problem 24

Find the next 3 numbers in these sequences: (a) 21, 16, 11, (b) $4, 12, 36, 108$ .

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Problem 25

Identify the pattern in the sequence $0, 3, 18, 57$ and extend it. Prove your conclusion using induction.

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Problem 26

Find the 37th term of an arithmetic sequence where $t_{1}=-3$ and $t_{2}=11$ .

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Problem 27

Calculate the 4-day moving average for days 4-12 of the DJIA. If day 13 closes at 20,660, should you buy or sell? Justify.

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Problem 28

Un paciente observa un ascensor que tarda 5 seg en moverse entre pisos y 20 seg al detenerse. ¿Cuánto tiempo estuvo observando?

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Problem 29

Find the number of dots in the 48th figure: $4(48)+2$ . Is there a figure with 200 dots? Explain. Total dots from 10th to 30th figure: $S=2m(m+1)$ .

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Problem 30

หาจำนวนรหัส 4 ตัวที่สร้างจากพยัญชนะ ก, ข, ค, ง โดยไม่ซ้ำกัน (24)

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Problem 31

Parents plan to deposit \$400 on their son's 10th birthday, increasing by \$50 yearly.
a. Find the deposit on his 20th birthday. b. Calculate total deposits by his 20th birthday.

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Problem 32

Find the 10th and 15th terms of the sequence $3, 7, 11, 15, 19, \ldots$

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Problem 33

Find the 7th and $n$ th terms of the sequence $5, 3, 1, -1, \ldots$

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Problem 34

Find the $r$ th term of the sequence: 72, 70, 68, 66, ...

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Problem 35

Find the fifteenth term of an A.P. where the 3rd term is 18 and the 7th term is 30.

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Problem 36

Find the $n$ th term of an A.P. where the 5th term is 38 and the 10th term is 23.

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Problem 37

Find the number of terms in the sequence $20, 18, 16, \ldots$ that ends with -4.

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Problem 38

Find the term number of the sequence $5, 14, 23, 32, \ldots$ that equals $239$ .

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Problem 39

Dado $A=1$ y $B=2$ , calcula los números $C$ , $D$ , y $E$ siguiendo el proceso de suma y división. Busca un patrón.

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Problem 40

Use the OPT replacement algorithm on the page references $0,6,3,0,2,6,3,5,2,4,1,3,0,6,1,4,2,3,5,7$ . How many page faults with 3 frames?

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Problem 41

Arrange 8 students with the following conditions: 1) A & B together: 10,080; 2) A & B at ends: 1,440; 3) A & B apart: 30,240; 4) Alternating genders: 1,152; 5) 4 boys & 4 girls together: 1,152.

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Problem 42

Select all possible outputs of the given C program when run on a Unix system. Possible outputs include:
1. ABBDD
2. A A B C D
3. A B D C D
4. ACBDD
5. ABBCCDD
6. ACD
7. A B C D
8. A B C D D

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Problem 43

Identify possible outputs of the given C program when run on a Unix system. Options include: ABBDD, A A B C D, A B D C D, ACBDD, ABBCCDD, ACD, A B C D, A B C D D.

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Problem 44

Find the next term in the sequence: 2, 2, 4, 6, 10, 16, 26, 42. Provide your answer as an integer, decimal, or E notation.

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Problem 45

Find the next term in the sequence: $343, 512, 729, 1000$ . Provide your answer in integer, decimal, or E notation.

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Problem 46

Find the next term in the sequence: 45, 94, 143, 192.

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Problem 47

Find the next term in the sequence: 55, 66, 78, 91.

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Problem 48

Match the sequences: $126,139,152,165,178$ ; $89,222.5,556.25,1390.625,3,476.5625$ ; $3,3,6,9,15,24$ ; $36,45,55,66,78$ ; $441,484,529,576,625$ with sequence types: Fibonacci, Arithmetic, Cube, Square, Geometric, Triangular.

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Problem 49

Check if these sequences are bounded:
1. $a_{n}=2+3 \cdot n$
2. $a_{n}=n-1$
3. $a_{n}=1-2 \cdot n$
4. $a_{n}=1$
5. $a_{n}=-5 \cdot n$
6. $a_{n}=0$

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Problem 50

Gegeben sind zwei Glieder einer geometrischen Folge. Finde $b_{0}$ , den Quotienten $q$ und die Formel für $b_{n}$ .
a) $b_{1}=98 ; b_{2}=686$ b) $b_{2}=216 ; b_{4}=7776$ c) $b_{3}=1875 ; b_{5}=46875$

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Problem 51

Untersuche, ob die Zahlenfolgen geometrisch sind. Wenn ja, gib die Formel an. Wenn nicht, wie kann man sie ändern?
a) $b_0 = 1$ , $b_1 = -2$ , $b_2 = 4$ b) $b_2 = 100$ , $b_4 = 4$ , $b_6 = 0.25$ c) $b_0 = 8$ , $b_2 = 18$ , $b_5 = 60.75$ d) $b_1 = -1$ , $b_2 = 1$ , $b_5 = 1$

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Problem 52

אורך הצלע הקצרה במלבן הרביעי בסדרה הוא מה? הסדרה מתחילה עם 1, 3, ו-6, והאורך מוכפל ב-2 בכל מלבן.

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Problem 53

Escribe los primeros 10 múltiplos de 61: $61 \times 1, 61 \times 2, \ldots, 61 \times 10$ .

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Problem 54

Escribe los primeros 10 múltiplos de 21: $21, 42, 63, 84, 105, 126, 147, 168, 189, 210$ .

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Problem 55

Gib die rekursive Darstellung der Folge $x_{n}$ für $x_{n}=2^{n+1}$ , $x_{n}=2n+1$ , und $x_{n}=(-1)^{n}$ an!

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Problem 56

Find the recursive formula for the sequence defined by $t_{n}=-5+(n-1) 78$ , with $n \in N$ and $n \geq 1$ .

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Problem 57

Find the next 3 terms in the sequence where $a_{n}=a_{n-1}+9$ and $a_1=-12$ . Choices: -3,-15,-27; B -3,6,15; -3,-6,-3; D -3,-6,3; -3,3,9.

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Problem 58

Find the next 3 terms of the sequence with $a_{1} = -12$ and $a_{n} = a_{n-1} + 9$ . Choices: A) -3,-15,-27 B) -3,6,15 C) -3,-6,-3 D) -3,-6,3 E) -3,3,9

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Problem 59

Identify the version of the sequence with an error among: 1) $f(x)=6 x+5$ , 2) $a_{1}=11$ , $a_{n+1}=a_{n}+6$ , 3) $a_{n}=11+6(n-1)$ . Fix it.

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Problem 60

Which TWO sequences are equivalent? A: $f(x)=7x-15$ B: $f(x)=7x-22$ C: $f(x)=7x-29$ D: $a_{1}=-22$ , $a_{n+1}=a_{n}+7$ E: $a_{1}=-29$ , $a_{n+1}=a_{n}+7$

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Problem 61

Find the limit as $n \to \infty$ of $\frac{\lfloor x \rfloor + \lfloor 2^2 x \rfloor + \ldots + \lfloor n^2 x \rfloor}{n^3}$ .

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Problem 62

Find the first three terms of a geometric sequence where the $5^{\text{th}}$ term is 1875 and the $7^{\text{th}}$ term is 46875.

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Problem 63

Find the next number in the series: $36, 34, 30, 28, 24, \ldots$ .

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Problem 64

Determine the common difference in the arithmetic sequence $11, 20, 29, \ldots$

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Problem 65

A Tik Tokker gains 20 more subscribers daily, starting with 100 on day 1. How many total subscribers after 5 days?

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Problem 66

Find an index $i$ in array $\mathrm{A}$ where the sum before $i$ equals the sum after $i$ . Return $-1$ if none exist.

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Problem 67

What is the next number in the sequence? $1, 2, 2, 4, 8, 32, ?$

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Problem 68

Find the next three numbers in the sequence: 47, 49, 51, 59.

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Problem 69

1) Find the expression for the sequence: -66, -132, -198, -264 with $n=1$ for the first term. $a_n=$
2) Find the expression for the sequence: 7, 14, 21, 28 with $n=1$ for the first term. $a_n=$

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Problem 70

3) Find the expression for the sequence -65, -64, -63, ... and calculate the $78^{\text{th}}$ term, $a_{78}$ .
4) Write the expression for the sequence 55, 110, ... and determine the $92^{\text{nd}}$ term, $a_{92}$ .

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Problem 71

Find a formula for the $n^{\text{th}}$ term $a_{n}$ of the sequence $16, 7, -2, \ldots$ .

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Problem 72

Find a formula for $a_{n}$ , the $n^{\text{th}}$ term of the sequence $36, 44, 52, \ldots$ .

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Problem 73

Find the formula for the $n^{\text{th}}$ term $a_{n}$ of the sequence: 6, 16, 26, ...

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Problem 74

Find the formula for $a_{n}$ , the $n^{\text{th}}$ term of the sequence $31, 27, 23, \ldots$

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Problem 75

Find the 70th term of the sequence $29, 17, 5, \ldots$

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Problem 76

Find the 52nd term of the sequence: $-8, -12, -16, \ldots$

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Problem 77

Find the 82nd term of the arithmetic sequence -10, 6, 22, ...

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Problem 78

Find a formula for the $n^{\text{th}}$ term $a_{n}$ of the sequence $3, -3, -9, \ldots$

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Problem 79

Find a formula for the $n^{\text{th}}$ term $a_{n}$ of the sequence: 23, 27, 31, ...

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Problem 80

Find the 100th and nth term for these sequences: a. $1, 5, 9, 13, \ldots$ b. $80, 110, 140, \ldots$ c. $1, 2, 4, \ldots$ d. $7, 7^{4}, 7^{7}, 7^{10}, \ldots$ e. $198 + 5 \cdot 2^{31}, 198 + 6 \cdot 2^{31}, 198 + 7 \cdot 2^{31}, \ldots$

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Problem 81

Find the 100th term of the sequence $7, 7^{4}, 7^{7}, 7^{10}, \ldots$ in exponential notation.

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Problem 82

Find the 100th term of the sequence $7, 7^{4}, 7^{7}, 7^{10}, \ldots$ and express it in exponential form.

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Problem 83

Find the nth term of the sequence $7, 7^{4}, 7^{7}, 7^{10}, \ldots$ and simplify your answer.

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Problem 84

Find the $n$ th term of the sequence: $198 + (n+4) \cdot 2^{31}$ .

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Problem 85

Find the next three terms in the sequence using a clock face: $2, 7, 12, 5, 10$ .

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Problem 86

How many terms are in these sequences? a. $35,36,37,\ldots,435$ b. $1,3,3^{2},\ldots,3^{60}$ c. $1000,2000,\ldots,500000$ d. $1,3,9,\ldots,6561$

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Problem 87

Find the number of marbles in the sixth line if each line follows the rule: $n_{k} = 2n_{k-1} - 1$ , starting with $n_1 = 2$ .

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Problem 88

Plot terms of the logistic equation $x_{t+1}=c x_t(1-x_t)$ with $x_0=0.4$ , $c=3.5$ . Check for convergence or divergence.

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Problem 89

Find the relationship between consecutive numbers in the sequence: $2, 6, 18, 54, 162, \ldots$

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Problem 90

Find the relationship between consecutive numbers in the sequence: $4, 12, 36, 108, 324, \ldots$

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Problem 91

What comes next in the series: a11, A12, b21, B22, c31, C32? A. $\mathrm{C} 33$ B. D33 C. $d 33$ D. $d 41$ E. D41 F. c33

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Problem 92

What comes next in the series? $10 \mathrm{~A}, 21 \mathrm{~b}, 32 \mathrm{C}, 43 \mathrm{~d}, 54 \mathrm{E}, 65 \mathrm{f}$ ? Options: A. $76 \mathrm{G}$ B. $66 \mathrm{~g}$ C. 765 D. $7 \mathrm{fg}$ E. $76 \mathrm{~g}$ F. $66 \mathrm{G}$

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Problem 93

What comes next in the series: $a 3 Z, b 6 Y, c 9 X, d 12 W, e 15 V, f 18 U$ ? Options: A. g21T B. $924 \mathrm{U}$ C. $\mathrm{G} 24 \mathrm{~T}$ D. $g 21 t$ E. $\mathrm{f} 21 \mathrm{~T}$ F. $g 24 t$

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Problem 94

Find the sixth term in the sequence starting with 5, where each term is $2 \times \text{previous} - 4$ .

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Problem 95

Find the number of marbles in the sixth line of a pattern starting with 10, decreasing by 1 each line.

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Problem 96

Find an equation for the sequence $7, 9, 11, 13, 15, \ldots$ and determine the 20th term.

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Problem 97

Find the next number in the sequence: $2, 6, 10, 14$ . Choices: a. 16, b. 17, c. 18, d. 20.

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Problem 98

Find the explicit formula for the sequence: 15, 19, 23, 27, ...

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Problem 99

Find the recursive formula for the sequence: 15, 19, 23, 27, ...

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Problem 100

Find the recursive formula for the sequence where $a_{1}=-1$ and $d=-10$ .

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Sequence

Problem 1

Find the limit of the sequence an=n2+3n−na_{n}=\sqrt{n^{2}+3 n}-nan​=n2+3n​−n. Options: A) 3 B) 2 C) 1/2 1 / 2 1/2 D) 3/2 3 / 2 3/2 E) 0 F) 1 G) ∞ \infty ∞ H) does not exist.

Problem 2

Ibrahim dan Zahra datang ke mesjid setiap 4 dan 6 hari. Apakah mereka bersama lagi pada 12, 14, dan 26 Juli 2022?

Problem 3

Ibrahim dan Zahra datang bersama pada 2 Juli 2022. Kapan mereka akan bersama lagi? Tandai dengan \sqrt{ }​ pilihanmu! 1. 12 Juli 2022 2. 14 Juli 2022 3. 26 Juli 2022 4. 7 Agustus 2022

Problem 4

Digite o número que falta na sequência: 1,2,□,8,16,321, 2, \square, 8, 16, 321,2,□,8,16,32.

Problem 5

Buat kesimpulan umum secara induksi untuk urutan nombor −12,32,256,…-\frac{1}{2}, \frac{3}{2}, \frac{25}{6}, \ldots−21​,23​,625​,… mengikut pola yang diberikan.

Problem 6

Calculate 12/2012 / 2012/20 and find the missing number in the sequence: 100, 93, 84, 73.

Problem 7

Find the next number in the sequence: 6,3,12,9,36,336, 3, 12, 9, 36, 336,3,12,9,36,33.

Problem 8

Find the next number in the sequence: 7, 11, 16, 22, 29, ?

Problem 9

Identify which sequence is arithmetic and which is geometric: Sequence #1: 5,15,45,135,4055, 15, 45, 135, 4055,15,45,135,405; Sequence #2: 5,15,25,35,455, 15, 25, 35, 455,15,25,35,45.

Problem 10

Compare the 15th 15^{\text {th }}15th term of the arithmetic sequence 150,650,1150,1650,...150,650,1150,1650,...150,650,1150,1650,... and geometric sequence 4,12,36,108,...4,12,36,108,...4,12,36,108,.... Show your work.

Problem 11

Compare the 15th15^{\text{th}}15th term of the sequences: Arithmetic: 150,650,1150,…150, 650, 1150, \ldots150,650,1150,… and Geometric: 4,12,36,…4, 12, 36, \ldots4,12,36,….

Problem 12

Find the 6th and 7th terms of the sequence 7n−57n-57n−5; also, find the sum of the 100th and 200th terms. Is 99 a term?

Problem 13

Find the 10th term of the sequence n2n^2n2 and the nnn where 2n2−16=n22n^2 - 16 = n^22n2−16=n2.

Problem 14

En la secuencia, cada número es la suma de los dos anteriores. ¿Cuál es el valor de xxx en la fila? 10, 16, 28, 26, 149.

Problem 15

En una secuencia, cada número se forma sumando los dos de arriba. ¿Qué valor tiene xxx si 26 = 10 + 16?

Problem 16

Problem 17

Find the missing numbers in the sequence 81, 82, 84, 86 on a number line from 81 to 100, increasing by 2 each time.

Problem 18

How much will Cardo save on the 9th day if he starts with \$75 and doubles his savings daily?

Problem 19

Identify the pattern starting with 5 that follows "subtract 2, then multiply by 3": a. 5,7,21,695,7,21,695,7,21,69 b. 5,2,4,1,25,2,4,1,25,2,4,1,2 c. 5,15,13,39,375,15,13,39,375,15,13,39,37 d. 5,3,9,7,21,195,3,9,7,21,195,3,9,7,21,19

Problem 20

Cari sebutan ke-nnn, TnT_{n}Tn​, dari pola: 5=3+2(1)5=3+2(1)5=3+2(1), 9=3+3(2)9=3+3(2)9=3+3(2), 15=3+4(3)15=3+4(3)15=3+4(3).

Problem 21

Find the common ratio rrr of the geometric sequence 7, 189, yyy, 1701. Then, determine the smallest integer nnn for which the nnn-th term exceeds 10,000.

Problem 22

Execute nnn processes with given times. When executing time[i], reduce all equal times to ⌈time[i]/2⌉\lceil \text{time}[i]/2 \rceil⌈time[i]/2⌉. Find total execution time.

Problem 23

Find the next number in the sequence: 3,4,1,8,5,2,9,10,1,?3,4,1,8,5,2,9,10,1, ?3,4,1,8,5,2,9,10,1,? a. 13 b. 6 c. 5 d. 7

Problem 24

Find the next 3 numbers in these sequences: (a) 21, 16, 11, (b) 4,12,36,1084, 12, 36, 1084,12,36,108.

Problem 25

Identify the pattern in the sequence 0,3,18,570, 3, 18, 570,3,18,57 and extend it. Prove your conclusion using induction.

Problem 26

Find the 37th term of an arithmetic sequence where t1=−3t_{1}=-3t1​=−3 and t2=11t_{2}=11t2​=11.

Problem 27

Calculate the 4-day moving average for days 4-12 of the DJIA. If day 13 closes at 20,660, should you buy or sell? Justify.

Problem 28

Un paciente observa un ascensor que tarda 5 seg en moverse entre pisos y 20 seg al detenerse. ¿Cuánto tiempo estuvo observando?

Problem 29

Find the number of dots in the 48th figure: 4(48)+24(48)+24(48)+2. Is there a figure with 200 dots? Explain. Total dots from 10th to 30th figure: S=2m(m+1)S=2m(m+1)S=2m(m+1).

Problem 30

หาจำนวนรหัส 4 ตัวที่สร้างจากพยัญชนะ ก, ข, ค, ง โดยไม่ซ้ำกัน (24)

Problem 31

Parents plan to deposit \$400 on their son's 10th birthday, increasing by \$50 yearly. a. Find the deposit on his 20th birthday. b. Calculate total deposits by his 20th birthday.

Problem 32

Find the 10th and 15th terms of the sequence 3,7,11,15,19,…3, 7, 11, 15, 19, \ldots3,7,11,15,19,…

Problem 33

Find the 7th and nnnth terms of the sequence 5,3,1,−1,…5, 3, 1, -1, \ldots5,3,1,−1,…

Problem 34

Find the rrrth term of the sequence: 72, 70, 68, 66, ...

Problem 35

Find the fifteenth term of an A.P. where the 3rd term is 18 and the 7th term is 30.

Problem 36

Find the nnnth term of an A.P. where the 5th term is 38 and the 10th term is 23.

Problem 37

Find the number of terms in the sequence 20,18,16,…20, 18, 16, \ldots20,18,16,… that ends with -4.

Problem 38

Find the term number of the sequence 5,14,23,32,…5, 14, 23, 32, \ldots5,14,23,32,… that equals 239239239.

Problem 39

Dado A=1A=1A=1 y B=2B=2B=2, calcula los números CCC, DDD, y EEE siguiendo el proceso de suma y división. Busca un patrón.

Problem 40

Use the OPT replacement algorithm on the page references 0,6,3,0,2,6,3,5,2,4,1,3,0,6,1,4,2,3,5,70,6,3,0,2,6,3,5,2,4,1,3,0,6,1,4,2,3,5,70,6,3,0,2,6,3,5,2,4,1,3,0,6,1,4,2,3,5,7. How many page faults with 3 frames?

Find the limit of the sequence $a_{n}=\sqrt{n^{2}+3 n}-n$ . Options: A) 3 B) 2 C) $1 / 2$ D) $3 / 2$ E) 0 F) 1 G) $\infty$ H) does not exist.

Ibrahim dan Zahra datang bersama pada 2 Juli 2022. Kapan mereka akan bersama lagi? Tandai dengan $\sqrt{ }$ pilihanmu!
1. 12 Juli 2022
2. 14 Juli 2022
3. 26 Juli 2022
4. 7 Agustus 2022

Digite o número que falta na sequência: $1, 2, \square, 8, 16, 32$ .

Buat kesimpulan umum secara induksi untuk urutan nombor $-\frac{1}{2}, \frac{3}{2}, \frac{25}{6}, \ldots$ mengikut pola yang diberikan.

Calculate $12 / 20$ and find the missing number in the sequence: 100, 93, 84, 73.

Find the next number in the sequence: $6, 3, 12, 9, 36, 33$ .

Identify which sequence is arithmetic and which is geometric: Sequence #1: $5, 15, 45, 135, 405$ ; Sequence #2: $5, 15, 25, 35, 45$ .

Compare the $15^{\text {th }}$ term of the arithmetic sequence $150,650,1150,1650,...$ and geometric sequence $4,12,36,108,...$ . Show your work.

Compare the $15^{\text{th}}$ term of the sequences: Arithmetic: $150, 650, 1150, \ldots$ and Geometric: $4, 12, 36, \ldots$ .

Find the 6th and 7th terms of the sequence $7n-5$ ; also, find the sum of the 100th and 200th terms. Is 99 a term?

Find the 10th term of the sequence $n^2$ and the $n$ where $2n^2 - 16 = n^2$ .

En la secuencia, cada número es la suma de los dos anteriores. ¿Cuál es el valor de $x$ en la fila? 10, 16, 28, 26, 149.

En una secuencia, cada número se forma sumando los dos de arriba. ¿Qué valor tiene $x$ si 26 = 10 + 16?

Identify the pattern starting with 5 that follows "subtract 2, then multiply by 3": a. $5,7,21,69$ b. $5,2,4,1,2$ c. $5,15,13,39,37$ d. $5,3,9,7,21,19$

Cari sebutan ke- $n$ , $T_{n}$ , dari pola: $5=3+2(1)$ , $9=3+3(2)$ , $15=3+4(3)$ .

Find the common ratio $r$ of the geometric sequence 7, 189, $y$ , 1701. Then, determine the smallest integer $n$ for which the $n$ -th term exceeds 10,000.

Execute $n$ processes with given times. When executing time[i], reduce all equal times to $\lceil \text{time}[i]/2 \rceil$ . Find total execution time.

Find the next number in the sequence: $3,4,1,8,5,2,9,10,1, ?$ a. 13 b. 6 c. 5 d. 7

Find the next 3 numbers in these sequences: (a) 21, 16, 11, (b) $4, 12, 36, 108$ .

Identify the pattern in the sequence $0, 3, 18, 57$ and extend it. Prove your conclusion using induction.

Find the 37th term of an arithmetic sequence where $t_{1}=-3$ and $t_{2}=11$ .

Find the number of dots in the 48th figure: $4(48)+2$ . Is there a figure with 200 dots? Explain. Total dots from 10th to 30th figure: $S=2m(m+1)$ .

Parents plan to deposit \$400 on their son's 10th birthday, increasing by \$50 yearly.
a. Find the deposit on his 20th birthday. b. Calculate total deposits by his 20th birthday.

Find the 10th and 15th terms of the sequence $3, 7, 11, 15, 19, \ldots$

Find the 7th and $n$ th terms of the sequence $5, 3, 1, -1, \ldots$

Find the $r$ th term of the sequence: 72, 70, 68, 66, ...

Find the $n$ th term of an A.P. where the 5th term is 38 and the 10th term is 23.

Find the number of terms in the sequence $20, 18, 16, \ldots$ that ends with -4.

Find the term number of the sequence $5, 14, 23, 32, \ldots$ that equals $239$ .

Dado $A=1$ y $B=2$ , calcula los números $C$ , $D$ , y $E$ siguiendo el proceso de suma y división. Busca un patrón.

Use the OPT replacement algorithm on the page references $0,6,3,0,2,6,3,5,2,4,1,3,0,6,1,4,2,3,5,7$ . How many page faults with 3 frames?

Select all possible outputs of the given C program when run on a Unix system. Possible outputs include:
1. ABBDD
2. A A B C D
3. A B D C D
4. ACBDD
5. ABBCCDD
6. ACD
7. A B C D
8. A B C D D

Find the next term in the sequence: $343, 512, 729, 1000$ . Provide your answer in integer, decimal, or E notation.

Check if these sequences are bounded:
1. $a_{n}=2+3 \cdot n$
2. $a_{n}=n-1$
3. $a_{n}=1-2 \cdot n$
4. $a_{n}=1$
5. $a_{n}=-5 \cdot n$
6. $a_{n}=0$

Escribe los primeros 10 múltiplos de 61: $61 \times 1, 61 \times 2, \ldots, 61 \times 10$ .

Escribe los primeros 10 múltiplos de 21: $21, 42, 63, 84, 105, 126, 147, 168, 189, 210$ .

Gib die rekursive Darstellung der Folge $x_{n}$ für $x_{n}=2^{n+1}$ , $x_{n}=2n+1$ , und $x_{n}=(-1)^{n}$ an!

Find the recursive formula for the sequence defined by $t_{n}=-5+(n-1) 78$ , with $n \in N$ and $n \geq 1$ .

Find the next 3 terms in the sequence where $a_{n}=a_{n-1}+9$ and $a_1=-12$ . Choices: -3,-15,-27; B -3,6,15; -3,-6,-3; D -3,-6,3; -3,3,9.

Find the next 3 terms of the sequence with $a_{1} = -12$ and $a_{n} = a_{n-1} + 9$ . Choices: A) -3,-15,-27 B) -3,6,15 C) -3,-6,-3 D) -3,-6,3 E) -3,3,9

Identify the version of the sequence with an error among: 1) $f(x)=6 x+5$ , 2) $a_{1}=11$ , $a_{n+1}=a_{n}+6$ , 3) $a_{n}=11+6(n-1)$ . Fix it.

Which TWO sequences are equivalent? A: $f(x)=7x-15$ B: $f(x)=7x-22$ C: $f(x)=7x-29$ D: $a_{1}=-22$ , $a_{n+1}=a_{n}+7$ E: $a_{1}=-29$ , $a_{n+1}=a_{n}+7$

Find the limit as $n \to \infty$ of $\frac{\lfloor x \rfloor + \lfloor 2^2 x \rfloor + \ldots + \lfloor n^2 x \rfloor}{n^3}$ .

Find the first three terms of a geometric sequence where the $5^{\text{th}}$ term is 1875 and the $7^{\text{th}}$ term is 46875.

Find the next number in the series: $36, 34, 30, 28, 24, \ldots$ .

Determine the common difference in the arithmetic sequence $11, 20, 29, \ldots$

Find an index $i$ in array $\mathrm{A}$ where the sum before $i$ equals the sum after $i$ . Return $-1$ if none exist.

What is the next number in the sequence? $1, 2, 2, 4, 8, 32, ?$

1) Find the expression for the sequence: -66, -132, -198, -264 with $n=1$ for the first term. $a_n=$
2) Find the expression for the sequence: 7, 14, 21, 28 with $n=1$ for the first term. $a_n=$

3) Find the expression for the sequence -65, -64, -63, ... and calculate the $78^{\text{th}}$ term, $a_{78}$ .
4) Write the expression for the sequence 55, 110, ... and determine the $92^{\text{nd}}$ term, $a_{92}$ .

Find a formula for the $n^{\text{th}}$ term $a_{n}$ of the sequence $16, 7, -2, \ldots$ .

Find a formula for $a_{n}$ , the $n^{\text{th}}$ term of the sequence $36, 44, 52, \ldots$ .

Find the formula for the $n^{\text{th}}$ term $a_{n}$ of the sequence: 6, 16, 26, ...

Find the formula for $a_{n}$ , the $n^{\text{th}}$ term of the sequence $31, 27, 23, \ldots$