Question

Which sequences are geometric sequences? 4, 2, 1,1/2,1/4,... −2, 3, −4, 5, −6, … 2, 6, 18, 54, 162, … −4, −16, −64, −256, … −2, −4, −12, −48, −240, …

Answer 1

first one: 4, 2, 1,1/2,1/4

third one: 2, 6, 18, 54, 162

fourth one: −4, −16, −64, −256

Explanation:

To know if a sequence is a geometric sequence, we divide a term by the term that goes before, and the resulting value will be the ratio and need to keep working on the next divisions of terms by the terms before.

Let's check each sequence:

4, 2, 1,1/2,1/4

2/4 = 0.5

1/2 = 0.5

1/2 / 1 = 0.5

1/4 / 1/2 = 0.5

This sequence is a geometric sequence, with ratio = 0.5

−2, 3, −4, 5, −6

3/-2 = -1.5

-4/3 = -1.333

This is not a geometric sequence

2, 6, 18, 54, 162

6/2 = 3

18/6 = 3

54/18 = 3

162/54 = 3

This sequence is a geometric sequence, with ratio = 3

−4, −16, −64, −256

-16/-4 = 4

-64/-16 = 4

-256/-64 = 4

This sequence is a geometric sequence, with ratio = 4

−2, −4, −12, −48, −240

-4/-2 = 2

-12/-4 = 3

This is not a geometric sequence