Question

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

-5

-2

2

5

Answer 1

Answer:

5

Step-by-step 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

$r=\frac{-10}{-2}=5$