Sequence & series

Q. Find the 10th term of the sequence defined by a_n = 3n + 2.

A. 32
B. 30
C. 28
D. 34

Solution

a_10 = 3(10) + 2 = 30 + 2 = 32.

Correct Answer: A — 32

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Q. Find the 10th term of the sequence defined by a_n = 3n^2 + 2n.

A. 320
B. 302
C. 290
D. 310

Solution

a_10 = 3(10^2) + 2(10) = 300 + 20 = 320.

Correct Answer: B — 302

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Q. If the first term of an arithmetic series is 5 and the common difference is 3, what is the 15th term?

A. 44
B. 45
C. 43
D. 42

Solution

a_n = a + (n-1)d = 5 + (15-1) * 3 = 5 + 42 = 47.

Correct Answer: A — 44

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Q. If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?

A. 20
B. 24
C. 16
D. 18

Solution

a_4 = 4^2 + 4 = 16 + 4 = 20.

Correct Answer: A — 20

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Q. If the sum of the first n terms of a geometric series is 81, and the first term is 3, what is the common ratio?

A. 2
B. 3
C. 4
D. 5

Solution

Using the formula S_n = a(1 - r^n) / (1 - r), we have 81 = 3(1 - r^n) / (1 - r). Solving gives r = 3.

Correct Answer: B — 3

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Q. If the sum of the first n terms of a geometric series is given by S_n = a(1 - r^n)/(1 - r), what is the sum when r = 1?

A. na
B. a
C. 0
D. undefined

Solution

When r = 1, S_n = a(1 - 1^n)/(1 - 1) is indeterminate, but the sum of n terms is na.

Correct Answer: A — na

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Q. If the sum of the first n terms of an arithmetic series is given by S_n = 3n^2 + 2n, what is the 4th term?

A. 26
B. 30
C. 22
D. 24

Solution

The 4th term a_4 = S_4 - S_3 = (3(4^2) + 2(4)) - (3(3^2) + 2(3)) = (48 + 8) - (27 + 6) = 56 - 33 = 23.

Correct Answer: A — 26

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Q. If the sum of the first n terms of an arithmetic series is given by S_n = 5n^2 + 3n, what is the 5th term?

A. 38
B. 43
C. 48
D. 53

Solution

The 5th term can be found using a_n = S_n - S_(n-1). Calculate S_5 and S_4, then find a_5 = S_5 - S_4 = (5(5^2) + 3(5)) - (5(4^2) + 3(4)) = 38.

Correct Answer: A — 38

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Q. In a geometric series, if the first term is 4 and the common ratio is 3, what is the 4th term?

A. 108
B. 81
C. 64
D. 48

Solution

The nth term of a geometric series is given by a_n = ar^(n-1). Thus, a_4 = 4 * 3^(4-1) = 4 * 27 = 108.

Correct Answer: A — 108

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Q. In a sequence defined by a_n = 2^n, what is the 5th term?

A. 16
B. 8
C. 32
D. 4

Solution

a_5 = 2^5 = 32.

Correct Answer: A — 16

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Q. In a sequence defined by a_n = 2^n, what is the value of a_5?

A. 32
B. 16
C. 64
D. 8

Solution

a_5 = 2^5 = 32.

Correct Answer: A — 32

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Q. In an arithmetic series, if the first term is 5 and the last term is 45, and there are 10 terms, what is the common difference?

A. 4
B. 5
C. 3
D. 2

Solution

Using the formula for the nth term: a_n = a + (n-1)d, we have 45 = 5 + 9d. Solving gives d = 4.

Correct Answer: A — 4

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Q. What is the 7th term of the sequence defined by a_n = 2^n + 3^n?

A. 2187
B. 243
C. 256
D. 729

Solution

a_7 = 2^7 + 3^7 = 128 + 2187 = 2315.

Correct Answer: A — 2187

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Q. What is the common ratio of the geometric series 4, 12, 36, ...?

A. 3
B. 2
C. 1.5
D. 4

Solution

The common ratio r = 12/4 = 3.

Correct Answer: A — 3

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Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?

A. 1.5
B. 2
C. 1
D. 3

Solution

S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.

Correct Answer: A — 1.5

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Q. What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?

A. 90
B. 100
C. 110
D. 120

Solution

The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.

Correct Answer: A — 90

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Q. What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?

A. n/2 * (2 + (n-1) * 3)
B. n * (2 + 3n)/2
C. 3n^2/2 + n/2
D. n * (n + 1)

Solution

The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).

Correct Answer: A — n/2 * (2 + (n-1) * 3)

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Q. What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?

A. 2
B. 1
C. 3
D. 4

Solution

The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.

Correct Answer: A — 2

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Showing 1 to 18 of 18 (1 Pages)

Sequence & series

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