Question

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

Answer 1

Answer:

$a_n=(-2)^{n-1}$

Step-by-step 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: $a_n=(-2)^{n-1}$