Free Printable Week 12 Quiz Review

1.

Which of the following functions shows an initial amount of $12 and an increase of 3.5% each year?

a)

y = 12(3.5)^x

b)

y = 12(1.035)^x

c)

y = 12(.035)^x

d)

y = 3.5(1.12)^x

2.

The population of Dawes County increases by 17% every year. If there are currently 185,000 people living there, what will be the population in 14 years?

If necessary, round your answer to the nearest whole number.

a)

9 people.

b)

20,606 people.

c)

1,666,379 people.

d)

1,716,146 people.

3.

Jacob deposited $800 in a savings account earning 5% interest, compounded quarterly. Which of the following equations could represent the amount of money in her account yearly?

a)

$A=800\left(1+\frac{0.5}{4}\right)^{4t}$

b)

$A=800\left(1+\frac{0.05}{4}\right)^{4t}$

c)

$A=800\left(1+\frac{0.05}{4}\right)^t$

d)

$A=800\left(1+\frac{5}{4}\right)^{4t}$

4.

John has $10,000 in a savings account that ears 15% interest, compounded monthly. To the nearest cent, how much will he have in 2 years?

a)

$53,502.50

b)

$13,225

c)

$10,251.62

d)

$13,473.51

5.

In the formula A = Pe^rt, A stands for

a)

Principal (Amount Invested)

b)

Interest Rate

c)

Final Amount

d)

Time

6.

Mariam put $7500 into an account paying 5% compounded continuously. She now has $9,630.19. How long has the money been in the account?

a)

7 years

b)

6 years

c)

5 years

d)

4 years

7.

Given an investment of $5,000:

Which investment would have a larger balance after 15 years?

Option 1 - 2% compounded annually

Option 2 - 1.9% compounded continuously.

a)

Option 1

b)

Option 2

8.

An amount of $25,000 is deposited into a bank paying an annual interest rate of 5.46% compounded continuously. How long will it take for the money to triple?

a)

21.22 years

b)

24.32 years

c)

20.12 years

d)

24.67 years

9.

Find the common ratio of the geometric sequence:
$2,\ \frac{1}{2},\ \frac{1}{8},\ \frac{1}{32},\ ...$

a)

$\frac{1}{3}$

b)

$\frac{1}{12}$

c)

$\frac{1}{16}$

d)

$\frac{1}{4}$

10.

Evaluate the geometric series described below.
$a_1=-1,\ r\ =\ 4,\ n\ =\ 8$

a)

-585

b)

585

c)

-21,845

d)

21,845

11.

What is the sum of the first ten terms of the sequence 4, -12, 36, -144 . . . ?

a)

59,050

b)

-59,048

c)

-78,732

d)

118,096

12.

Evaluate $\sum_{k\ =\ 1}^7\left(-2\right)^{k\ -1\ }$

a)

44

b)

$\frac{1}{3}$

c)

43

d)

49

13.

Find the sum of the infinite geometric series:

200 - 100 + 50 - 25 + ...

a)

525 / 2

b)

400 / 3

c)

3 / 400

d)

2 / 525

14.

Is the sequence -432, 72, -12, 2,...geometric?

a)

yes

b)

no

15.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

16.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

17.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

18.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

a)

-177,147

b)

-19,683

c)

-59,049

d)

118,098

19.

Find the sum of the geometric series.

a)

732

b)

-732

c)

244

d)

-244

20.

Find the explicit rule for the nth term of the sequence. The second and fifth terms of a geometric sequence are -24 and 1536, respectively.

a)

a_n= 6(-4)^n-1

b)

a_n= 6×-4^n-1

c)

a_n= 6(-4)ⁿ

d)

a_n= -6(4)^n-1

21.

Find the sum of the infinite geometric series, if it exists:

5 + 4 + 3.2 + 2.56 + ...

a)

25

b)

30

c)

-1

d)

0.8

22.

What is the sum of the first 10 terms for the following geometric series:
2-6+18-54+...

a)

59048

b)

-29524

c)

524288

d)

3069

23.

Find the sum for the following series.

a)

1.49

b)

3.14

c)

1.33

d)

1.66

24.

Is the sequence 2, 4, 12, 48,... geometric?

a)

yes

b)

no

25.

Find the 13th term:
2, 6, 18, 54, ….

a)

1,000,000

b)

1,062,882

c)

123,587

d)

5 bazillion

26.

Find the sum of the first 9 terms: -2 + -6 + -18 + ...

a)

-59,048

b)

-39,366

c)

-19,682

d)

-4,374

27.

$a_n=a_1r^{n-1}$

Find the 7th term in the sequence when the first term is 2, and the common ratio is 4

a)

8192

b)

32768

c)

2048

d)

512

28.

Find the sum of the infinite geometric series, if it exists:

-3 + -3/2 + -3/4 + -3/8...

a)

-6

b)

-8

c)

no sum

d)

-4

29.

In a geometric sequence, the 4th term is -12 and the 5th term is -24. Find the common ratio.

a)

2

b)

-2

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

30.

The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term.

a)

5

b)

6

c)

7

d)

8

31.

Neisha's salary for her first year was $44,000. She earned raises of 3% each year. What was her salary in her 10th year at the company? Round to the nearest dollar.

a)

$44,001

b)

$55,080

c)

$57,410

d)

$59,132

32.

What is the 8^th term in the geometric sequence ?

a)

49,152

b)

196,608

c)

12,288

d)

8748

33.

Find the missing term of the geometric sequence: 45, ______, 1620

a)

9720

b)

51

c)

6

d)

270

34.

What is the common ratio of the geometric sequence whose first term is 5 and third term in 245?

a)

7

b)

49

c)

120

d)

240

35.

$a_n=a_1r^{n-1}$

Consider the first six terms of this sequence : 3,6,12,24,48,96….. What would be the 19th term of the sequence

a)

393216

b)

786432

c)

1572864

d)

1162261467

36.

Is it possible to find the sum of all terms of the infinite geometric series with a₁ = 7 and r = -(5/4)?

a)

yes

b)

no

37.

Determine the $a_1$ and r value for a geometric sequence where: $a_3=45$ and $\ a_7=3645$

a)

$a_1=45$ , r = 7

b)

$a_1=5$ , r = 3

c)

$a_1=5$ , r = 81

d)

$a_1=3645$ ,

r = 45

38.

How many terms are in the geometric sequence

2, 6, 18, . . . , 1458

a)

n = 5

b)

n = 6

c)

n = 7

d)

n = 486

39.

The third term of a geometric sequence is 96 and the fifth term is 1536. What is the sum of the first ten terms of the sequence?

a)

4,092

b)

1,572,864

c)

2,097,150

d)

33,554,400

40.

Which statement is true about the series shown below?
-4 + -2 + -1 + ½ + -¼+ ...

a)

The series converges because ∣r∣ < 1

b)

The series diverges because ∣r∣ < 1

c)

The series converges because ∣r∣ > 1

d)

The series diverges because ∣r∣ > 1

41.

Evaluate the geometric series below:
-4 - 8 - 16 - 32..., S₆

a)

-253

b)

-252

c)

4

d)

-235

42.

Determine the number of terms, n , for the given finite geometric sequence.

a)

6

b)

5

c)

4

d)

3

43.

Find the sum.

24+48+72+...+480

*Hint: Find out what term number 480 is first. Then find the sum.*

a)

5280

b)

9576

c)

10080

d)

5040

44.

Determine the number of terms, n , in the given finite geometric sequence.

a)

3

b)

4

c)

5

d)

6

45.

Evaluate the series, if possible.

a)

64

b)

128

c)

256

d)

Not Possible

46.

A bouncing ball reaches heights of 16 cm, 12.8 cm, and 10.24 cm on three consecutive bounces. If the ball was originally dropped from 25 cm (a₁ = 25), how much total distance in the downward direction has the ball traveled after five bounces?

a)

25 cm

b)

84.04 cm

c)

53.7956 cm

d)

59.04 cm

47.

$a_1=-2,\ \ \ r=-2,\ \ \ S_n=-22$ Determine the number of terms n in the series

a)

6

b)

7

c)

8

d)

5

48.

Determine the sum of the finite geometric sequence.

a)

13,120

b)

13,021

c)

12,031

d)

11,320

Week 12 Quiz Review

Total questions: 48

Worksheet time: 4hrs 52mins

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