Free Printable geometric

1.

Find the common ratio: 16, 8, 4, 2, ...

a)

r = 2

b)

r = 8

c)

r = 1/4

d)

r = 1/2

2.

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

3.

The next term of the sequence 2,4,8,16 is

a)

64

b)

32

c)

108

d)

20

4.

Find the 10th term of the following geometric sequence

5, 20, 80, 320, ...

a)

81,920

b)

327,680

c)

1,310,720

d)

5,242,880

5.

What would be the missing terms of the series

-1 ,- 5, - 25 ,- ... ,- 78125

a)

125 , 625 , - 3125 , 15625

b)

125 , - 625 , - 15625

c)

125 , - 625 , - 3125 , - 15625

d)

625 , - 3125 , - 15625

6.

Given the formula for a geometric sequence, $a_1$ stands for $a_n=a_1r^{n-1}$

a)

common difference

b)

wanted term

c)

common ratio

d)

first term

7.

$a_n=a_1r^{n-1}$

Given the formula for a geometric sequence , r stands for

a)

common difference

b)

wanted term

c)

common ratio

d)

first term

8.

$a_n=a_1r^{n-1}$

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

9.

What is the 14th term of the geometric sequence?

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

10.

An infinite series exists for which of the following situations?

a)

An arithmetic series

b)

A geometric series

c)

A geometric series with | r | > 1

d)

A geometric series with | r | < 1

11.

The n^th term of a geometric sequence is given by ...

a)

b)

c)

d)

12.

The sum of an finite Geometric series is given by:

a)

b)

c)

d)

13.

The sum of an infinite Geometric series is given by:

a)

b)

c)

d)

14.

List the first five terms of the geometric sequence. Assume that the sequence begins at n = 1.

a)

1 , 3 , 6 , 9 , 12

b)

3 , 9 , 27 , 81 , 243

c)

0 , 1 , 3 , 9 , 27

d)

1 , 3 , 9 , 27 , 81

15.

Is the sequence geometric or not? If not, type NOT GEOMETRIC. If yes, determine the common ratio.

7, 14, 21, 28,...

(a)

16.

Is the sequence geometric or not. If not, type NOT GEOMETRIC. If yes, determine the common ratio.

64, 32, 16, 8,...

(a)

17.

What is the next term in the geometric sequence, $\frac{2}{3},\ 4,\ 24,\ 144,\ ...$ ?

(a)

18.

What is the next term in the geometric sequence, $9,\ 3,\ 1,\ \frac{1}{3},...$ ?

(a)

19.

Click TRUE if the statement is always true, otherwise, click FALSE.

If the terms are increasing, then the common ratio is less than zero.

a)

TRUE

b)

FALSE

20.

Click TRUE if the statement is always true, otherwise, click FALSE.

If\ \ \ a_{1\ }>a_{2\ }

then the common ratio is less than 1.

a)

TRUE

b)

FALSE

21.

Which is the explicit formula of the

geometric sequence $2,\ \frac{1}{4},\ \frac{1}{32},\ \frac{1}{256},...$ ?

a)

$a_n=2\left(\frac{1}{8}\right)^{n-1}$

b)

$a_n=2\left(\frac{1}{8}\right)^n$

c)

$a_n=2\left(8\right)^{n-1}$

d)

$a_n=2\left(8\right)^n$

22.

What is the 9th term of the geometric
sequence in which $a_1=\frac{3}{8}\ \ \ and\ \ \ r=-2$ ?

(a)

23.

Find the ratio of the geometric

sequence: –3, __, __, 648, …

(a)

24.

The given sequence –36, 6k, –9, … is geometric. Find k.

a)

3

b)

–3

c)

$\pm3$

d)

$\pm\frac{1}{3}$

25.

$If\ \ \ a_1=6\ \ \ and\ \ \ r=-2,\ \ \ find\ \ \ S_9.$

(a)

26.

What is the sum of the first 5 terms of

the geometric sequence with $a_3=12\ and\ a_5=48$ ?

a)

93

b)

33

c)

93 or 33

d)

-93 or -33

27.

What is the partial sum of the geometric

sequence, 2 + 6 + 18 + … + 1458 ?

(a)

28.

The first term of a geometric sequence is –3. Each term is doubled to determine the next term. If the sum of the first n terms of this sequence is –189, how many terms were added?

(a)

29.

A certain town has a total population of 280,000 people in 2014, if it increases 15% every 2 years, then what is the population in 2020?

(a)

30.

If you save Php 50 in January and you double your savings every month, how much will you have at the end of the year?

(a)

31.

$-3,\ \ 6,\ -12,\ \ 24,\ ....$ Find the common ratio

a)

3

b)

-2

c)

2

d)

$\frac{1}{2}$

32.

Evaluate the geometric series described.
$3+15+75+375...,\ \ \ \ n=6$

a)

11,718

b)

10,603

c)

9,769

d)

$-\frac{3}{4}$

33.

Which of the following four numbers are geometric means of 2, ______, _______, _______, _______, 64?

a)

4, 10, 28, 40

b)

4, 8, 16, 32,

c)

4, 8, 12, 20

d)

8, 14, 20, 32

34.

Which of the following four numbers are geometric means of 1, ______, _______, ______, ______, 3,125?

a)

-5, 25, -125, 625

b)

10, 50, 250, 2525

c)

5, 25, 125, 625

d)

25, 250, 1250, 2,125

35.

Insert one geometric mean between -4 and -100.

a)

-15

b)

-20

c)

-25

d)

-50

36.

Which of the following should be inserted between 3 and 192 to make a geometric sequence?

a)

12, 48

b)

16, 32

c)

14, 38

d)

12, 36

37.

Find the sum of the first 6 terms of the sequence 1, 2, 4, 8, ...

a)

61

b)

62

c)

63

d)

64

38.

Find the sum of the first 7 terms of a geometric series whose common ratio is -2 and whose first term is -3.

a)

-129

b)

-130

c)

-131

d)

-132

39.

How many terms are there in the geometric series $-2+6-18...$ if the sum is 364.

a)

5

b)

6

c)

7

d)

8

40.

Find the sum of the infinite series $6+2+\frac{2}{3}+\frac{2}{9}...$

a)

9

b)

10

c)

11

d)

No sum

41.

Find the sum of the infinite series $2-8+32-128...$

a)

$\frac{1}{5}$

b)

$\frac{2}{5}$

c)

$2$

d)

No sum

42.

How do you get the common ratio of the given geometric sequence?

a)

$\frac{a_2}{a_3}$

b)

$\frac{a_2}{a_1}$

c)

$\frac{a_1}{a_2}$

d)

$a_{1\ }+\ a_2$

43.

What is the common ratio of the given sequence 3,9,27,81

a)

4

b)

2

c)

6

d)

3

44.

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

a)

6

b)

7

c)

8

d)

5

45.

$-4,\ -12,\ -36,\ -108,\ ...$ Find the common ratio

a)

$r=-2$

b)

$r=-3$

c)

$r=3$

d)

$r=2$

geometric

Total questions: 45

Worksheet time: 2hrs 30mins

Similar Resources on Wayground