Question

Find the nth term an of the geometric sequence described below, where r is the common ratio.

a4 = -8, r= -2

Answer 1

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

Explanation:

So a geometric sequence can be explicitly defined as:
`a_n = a_1(r)^(n-1)`. IN this case we're given r, but we don't know what a_1 is. We can find this by lugging in 4 as n, and -8 as a_n, since they're given values

Plug known values in:

`-8 = a_1(-2)^(4-1)`

Subtract the values in the exponent

`-8 = a_1(-2)^3`

Simplify the exponent

`-8 = a_1 (-8)`

Divide both sides by -8

`1=a_1`

So the nth term can be defined as:
`a_n = 1(-2)^(n-1)`, and since the 1 is redundant, the equation can simply be defined as:
`a_n=(-2)^(n-1)`