Geometric Sequence

Geometric Identification

2

Determine whether the sequence is a geometric sequence...

5, 10, 15, 20

no

4

Determine whether the sequence is a geometric sequence...

4, 12, 36, 108...

yes, r=3

6

Determine whether the sequence is a geometric sequence...

120, -60, 30, -15...

yes, r=-1/2

8

Determine whether the sequence is a geometric sequence...

1, -4, 16, -64...

yes, r=-4

10

Determine whether the sequence is a geometric sequence...

625, -125, 25, 5, ...

no

Sequence Prediction

2

Find the next three terms of the geometric sequence

4, 8, 16, ...

32, 64, 128

4

Find the next three terms of the geometric sequence

3, 15, 75

375, 1875, 9375

6

Find the first three terms of the geometric sequence if

a₁ = −4, r = 6

-4, −24, −144

8

Find the first five terms of the geometric sequence whose a₁ = 4, r = 5

4, 20, 100, 500, 2500

10

Find the first five terms of the geometric sequence whose a₄ = 25, r = −5

−0.2, 1, −5, 25, −125

Geometric Sequence Analysis

2

How do you find the common ratio of a given geometric sequence?

By dividing each term by it's previous term.

4

Determine the common ratio for the following sequence: 135, 45, 15, 5, ...

r=1/3

6

Determine the common ratio for the following sequence: 7, -14, 28, -56...

r=-2

8

Given the sequence whose first term is -1 and the 4th term is -27, find the common ratio.

r=3

10

Find the common ratio of the geometric sequence whose 

a₅ = 768 and a₂ = 12

r=4

Geometric Term Finder

2

Given the sequence: -4, 20, -100, ... Find a₃

-100

4

Find the first term of the geometric sequence whose

a₄ = −12 and a₅ = −6.

a₁ = −96

6

Find the first term of the geometric sequence whose 

a₅ = 768 and a₂ = 12

a₁ = 3

8

Given the geometric sequence: -1, -4, -16... Find a₁₀

-262,144

10

A ball is dropped. Its first bounce is 400 feet high. It's second bounce is 320 feet high. Its third bounce is 256 feet high. Find the height of its twenty-eighth bounce to the nearest hundredth.

.97 ft

Geometric Mean Identification

2

Find the missing term/s of the geometric sequence

−3, ___, −108

-18 or 18

4

Find the missing term/s of the geometric sequence

1.5, ___, 6

3 or -3

6

Given the sequence whose first term is -1 and the 4th term is -27, find the second geometric mean.

-9

8

Insert 2 geometric means between 3 and 648.

18, 108

10

Insert 3 geometric means between 1 and 16 and identify the 2nd mean.

4