Deck 14: Section 2: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Question 1

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

Answer 1

Question 2

Write the given series in summation notation. Use the index i, and let i begin at 1.
ln(6) + ln(7) + ln(8)

Answer 2

ln(i + 5)

Question 3

Find the sum of the given infinite geometric series.

Answer 3

Question 4

Find the sum of the given series.

Question 5

Find r for the geometric sequence that has a₁ = 3 and a₄ = 192.

Question 6

Write a formula for the general term of the given sequence and match your result to the correct answer below.
-4, -3, -2, -1, 0, ...

Question 7

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

Question 8

List all terms of the finite sequence a_n = 3n + 2 for 1 ≤ n ≤ 5.

Question 9

List the first four terms of the given sequence and match your result to the correct answer below.
c_n = (-1)ⁿ(-4n + 3)²

Question 10

Find the sum of the given geometric series.

Question 11

Find .

Question 12

List all terms of the given finite sequence and match your result to the correct answer below.
c_n = (-2)^n-3 for 3 $\le$ n $\le$ 7

Question 13

Write the first five terms of the arithmetic sequence whose nth term is given.
a_n = -1 + (n + 1)(2)

Question 14

Write a formula for the nth term of the given geometric sequence.
3, -9, 27, ...

Question 15

Find .

Question 16

Write the first four terms of the geometric sequence whose nth term is given.
a_n = (-3)^n-1

Question 17

Suppose a deposit of $2000 is made at the beginning of each year for 45 years into an account that pays 11% compounded annually. What is the amount of this annuity at the end of the 45^th year?

Question 18

Evaluate .

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 80% efficient, what percent of the original material remains if a can is recycled 3 times? Round to the nearest tenth of a percent.

Question 20

Write a formula for the nth term of the given arithmetic sequence.
1, 7, 13, 19, 25, . . .

Question 21

Use the binomial theorem to write out the first four terms of the given binomial.
(x² + 1)²²