Question

Given that aₙ = (-2) (5)ⁿ⁻1 for a geometric sequence, determine the common ratio:

-5

-2

2

5

Answer 1

5

Explanation:

The nth term of the geometric sequence is

`a_n=(-2)(5)^(n-1)`

In general the nth term of a geometric sequence is

`a_n=a_1(r)^(n-1)`

By comparism;

`r=5` is the common ratio of the sequence.

Or

`a_1=(-2)(5)^(1-1)=-2`

`a_2=(-2)(5)^(2-1)=-10`

Common ratio is

`r=(-10)/(-2)=5`