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Question : 8) A woman borrowed $ 10,000 at 14% interest compounded annually. : 2151831

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Use the formula for S _{n} to find the sum for the geometric sequence.**

1) 2, 6, 18, 54, 162

A) 252

B) 242

C) 245

D) 240

2) 3, -9, 27, -81, 243

A) 183

B) -363

C) 363

D) -183

3) (2/3), (4/3), (8/3), (16/3), (32/3)

A) (62/3)

B) (64/3)

C) (60/3)

D) 21

4) 3, (3/2), (3/4), (3/8), (3/16)

A) (93/16)

B) (31/16)

C) (45/16)

D) (45/8)

5)

A) 42

B) 255

C) 186

D) 22

6)

A) -732

B) 240

C) -2,460

D) 69

7)

A) (5,456/3)

B) (5,474/3)

C) (5,483/3)

D) (5,405/3)

**Solve the problem.**

8) A woman borrowed $ 10,000 at 14% interest compounded annually. If the loan was paid off at the end of 6 years, how much did she pay? Round your answer to the nearest cent.

A) $ 18,400.00

B) $ 11,949.73

C) $ 11,400.00

D) $ 21,949.73

9) A man borrowed $ 2,000 at 10% interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay? Round your answer to the nearest cent.

A) $ 3,543.12

B) $ 2,200.00

C) $ 1,543.12

D) $ 3,200.00

10) Cathy May deposits $ 20,000 at the end of each year for 9 years in an account paying 7% compounded annually. She then puts the total amount on deposit in another account paying 8% compounded semiannually for another 10 years. Find the final amount on deposit after the entire 19-year period. Round your answer to the nearest cent.

A) $ 1,116,577.84

B) $ 354,606.99

C) $ 476,673.37

D) $ 524,904.97

11) Suppose you invest $ 8,393 at the end of each year into an account earning 8% interest (compounded annually). At the end of 8 years, how much money will be in the account?

A) $ 89,273.20

B) $ 88,974.60

C) $ 87,784.50

D) $ 194,185.70

12) A certain ball when dropped from a height rebounds 7/10 of the original height. How high will the ball rebound after the fifth bounce if it was dropped from a height of 32 feet? Round your answer to the nearest tenth of a foot.

A) 6.7 ft

B) 7.7 ft

C) 5.4 ft

D) 3.4 ft

**Find the sum, if it exists, of the terms of the infinite geometric sequence.**

13) a_{1} = 4, r = 3

A) 2187

B) 1024

C) 4096

D) Does not exist

14) a_{1} = 1, r = 1/4

A) (4/3)

B) (4/7)

C) (3/4)

D) Does not exist

15) a_{1} = 5, r = - 1/3

A) (15/2)

B) (15/4)

C) (10/3)

D) Does not exist

16) a_{1} = 13, r = 1/5

A) (13/4)

B) (13/6)

C) (65/6)

D) (65/4)

17)

A) 3072

B) 1886

C) 3441

D) Does not exist

18)

A) 3/2

B) 1

C) 2

D) Does not exist

19)

A) 3/5

B) -1

C) – 3/5

D) Does not exist

20)

A) (2/3)

B) (1/2)

C) (1/3)

D) Does not exist

21)

A) (4/3)

B) (1/4)

C) 1

D) Does not exist

22)

A) (220/9)

B) - (55/9)

C) (11/6)

D) Does not exist

**Solve the problem.**

23) A certain ball when dropped from a height rebounds 7/10 of the original height. How high will the ball rebound after the fifth bounce if it was dropped from a height of 32 feet? Round your answer to the nearest tenth of a foot.

A) 3.4 ft

B) 7.7 ft

C) 6.7 ft

D) 5.4 ft

24) A ball is dropped from a height of 47 feet. On each bounce, it bounces to 87% of its previous height. How high does it get after the 4th bounce? (Round to the nearest hundredth, if necessary.)

A) 361.54 feet

B) 30.95 feet

C) 154.41 feet

D) 26.93 feet

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

**Provide an appropriate response.**

25) For the sequence 3, 6, 12, 24, . . . , how would you determine each term after the first by using the previous term of the sequence?

26) If a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, . . . is a geometric sequence with common ratio r, show that a_{1}, a_{4}, a_{7}, a_{10} is a geometric sequence.

27) Give an example of a geometric sequence with a_{4} = 2,058.

28) How do you determine the common ratio of a geometric sequence?

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

29) Which of the following sequences is not a geometric sequence?

A) 1, -3, 9, -27, . . .

B) 4, (4/3), (4/9), (4/27)

C) 8, 80, 800, 8,000

D) 1, 2, 4, 7, 11, . . .

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

30) Is the following sequence geometric? Explain.

log_{6}, log_{6}^{2}, log_{6}^{4}, log6^{8}, . . .