Deck 14: Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Question 1

Write a formula for the nth term of the given arithmetic sequence. 4, 10, 16, 22, 28, . . .

A) a_n = 6n - 2
B) a_n = 7n - 3
C) a_n = 6n + 2
D) a_n = 2n - 6

Answer 1

a_n = 6n - 2

Question 2

Complete the rewriting of the given series using the new index as indicated.

A)

B)

C)

D)

Answer 2

Question 3

Evaluate .

A) 1
B) Undefined
C) 6
D) 0

Answer 3

1

Question 4

Suppose a deposit of $500 is made at the beginning of each year for 15 years into an account that pays 9% compounded annually. What is the amount of this annuity at the end of the 15^th year?

A) $16,501.70
B) $18,486.85
C) $13,009.59
D) $16,001.70

Question 5

Find the sum of the given geometric series.

A) -19,682
B) -59,048
C) -177,146
D) -6,560

Question 6

Find the sum of the given infinite geometric series.

A)
B)
C)
D)

Question 7

Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -3 + (n - 2)(-3)

A) -6, -3, 0, 3, 6
B) 3, 0, -3, -6.0, -9
C) 3, 0, -3, -6, -9
D) 0, -3, -6, -9, -12

Question 8

Use the binomial theorem to expand the given binomial. (t + 2)⁴

A) t⁴ + 8t³ + 12t² + 8t + 2
B) t⁴ + 8t³ + 24t² + 32t + 16
C) 2t⁴ + 16t³ + 48t² + 16t + 2
D) t⁴ + 2t³ + 4t² + 8t + 16

Question 9

Find the common difference of an arithmetic sequence if the first term is -9 and the seventh term is -39.

A) -4
B) 3
C) -6
D) -5

Question 10

Write the first four terms of the geometric sequence whose nth term is given. a_n = (-6)^n-1

A) 1, -6, 36, -216
B) 0, -6, 36, -216
C) 1, 6, 36, 216
D) -6, 36, -216, 1296

Question 11

Find .

A) -13
B) 13
C) 0
D) -1

Question 12

Find .

A) 24
B) 70
C) 14
D) 18

Question 13

List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1)ⁿ(-2n + 3)²

A) 1, -1, 9, -25
B) 1, -1, 1, -9
C) 1, -9, 25, -49
D) -1, 1, -9, 25

Question 14

List all terms of the given finite sequence and match your result to the correct answer below. c_n = (-1)^n-3 for 3  n  7

A) -1, 1, -1, 1, -1
B) 1, 1, 1, 1, 1
C) 1, -1, -1, -1, -1
D) 1, -1, 1, -1, 1

Question 15

Write the given series in summation notation. Use the index i, and let i begin at 1. ln(9) + ln(10) + ln(11)

A) ln(i + 9)
B) ln(i + 8)
C) ln(i)
D) ln(i + 7)

Question 16

Find the sum of the given series.

A) 9
B) -27
C) -108
D) -36

Question 17

Write a formula for the nth term of the given geometric sequence. 3, -6, 12, ...

A) a_n = -3(2)^n-1
B) a_n = 3(-2)ⁿ⁺¹
C) a_n = 3(-2)^n-1
D) a_n = 3(-2)ⁿ

Question 18

List all terms of the finite sequence a_n = 6n + 2 for 1 ≤ n ≤ 5.

A) 8, 14, 20, 26, 32
B) 8, 10, 12, 14, 16
C) 9, 10, 11, 12, 13
D) 1, 2, 3, 4, 5

Question 19

Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 90% efficient, what percent of the original material remains if a can is recycled 6 times? Round to the nearest tenth of a percent.

A) 63.2%
B) 56.5%
C) 57.9%
D) 53.1%

Question 20

Write a formula for the general term of the given sequence and match your result to the correct answer below. -2, -1, 0, 1, 2, ...

A) a_n = (-1)ⁿ(n - 3)
B) a_n = n - 3
C) a_n = -n - 3
D) a_n = n + 3

Question 21

Use the binomial theorem to write out the first four terms of the given binomial. (x² + 1)¹⁷

A) x¹⁷ + 17x¹⁶ + 136x¹⁵ + 680x¹⁴
B) x³⁴ + 17x³² + 136x³⁰ + 680x²⁸
C) x¹⁷ + 17x³³ + 136x³² + 680x³¹
D) x³⁴ + 17x³³ + 136x³² + 680x³¹