# Geometric Sequences Exercises

### Example 1

Determine whether the sequence is geometric.

1,

### Example 2

Determine whether the sequence is geometric.

3,6,9,12,...

### Example 3

Determine whether the sequence is geometric.

10, 15, 22.5, 33.75, ...

### Example 4

Determine whether the sequence is geometric.

3, 12, 48, 192, ...

### Example 5

Determine whether the sequence is geometric.

.9, .8, .7, .6, ...

### Example 6

Determine if the sequence is geometric or not.

1,-1,1,-1,...

### Example 7

Determine if the sequence is geometric or not.

-2,14,-98, 686, ...

### Example 8

Determine if the sequence is geometric or not.

3, -15, -75, 375, ...

### Example 9

Find the first four terms of the geometric sequence with

*a*_{1} = 7 and *r* = 3

### Example 10

Find the first four terms of the geometric sequence with

*a*_{1} = 100 and

### Example 11

Find the first four terms of the geometric sequence with

*a*_{1} = 2 and *r* = 0.5

### Example 12

Find the first four terms of the geometric sequence with

*a*_{1} = 8 and *r* = -4

### Example 13

Find the first four terms of the geometric sequence with

*a*_{1} = 3 and *r* = 1

### Example 14

A geometric sequence has *a*_{1} = 4 and *r* = 5. Find

a) *a*_{2}

b) *a*_{3}

c) *a*_{4}

d) *a _{n}*

### Example 15

A geometric sequence has *a*_{1} = 3 and . Find

a) *a*_{2}

b) *a*_{3}

c) *a*_{4}

d) *a _{n}*

### Example 16

A general geometric sequence has first term *a*_{1} and common ratio *r*. Find

a) *a*_{2}

b) *a*_{3}

c) *a*_{4}

d) *a _{n}*, the general formula for the

*n*

^{th}term.

### Example 17

A geometric sequence has *a* = 8 and *r* = 0.2. Find *a*_{5}.

### Example 18

A geometric sequence has *a* = 2 and *r* = -5. Find *a*_{7}.

### Example 19

A geometric sequence has *a* = 0.125 and *r* = 2. Find *a*_{20}.

### Example 20

Find *a* and *r* for the geometric sequence with the given terms.

*a*_{7} = 640 and *a*_{8} = -1280

### Example 21

Find *a* and *r* for the geometric sequence with the given terms.

*a*_{4} = 1.2 and *a*_{5} = 0.24

### Example 22

Find *a* and *r* for the geometric sequence with the given terms.

*a*_{4} = -3.125 and *a*_{5} = 0.78125

### Example 23

Find *a* and *r* for the geometric sequence with the given terms.

*a*_{11} = 1 and *a*_{13} = 0.0625

### Example 24

Find *a* and *r* for the geometric sequence with the given terms.

*a*_{4} = 51.2 and *a*_{7} = 26.2144