## Algebra 2 Common Core

$0.0018310546875$
Recall the formula for the $n^{\text{th}}$ term of a geometric sequence: $a_{n}=$ $a_{1}$ $\times$ $r^{n-1}$ where $a_n$ = $n^{\text{th}}$ term; $a_1$ = first term; $n$ = term number' $r$ = common ratio The given geometric sequence has: $a_{1}=-30$ , $n=8$ and $r=\dfrac{7.5}{-30}=-0.25$: Substituting these values into the formula above gives: $a_{8}=$ $-30$ $\times$ $(-0.25)^{8-1}$ $a_{8}=$ $-30$ $\times$ $(-0.25)^{7}$ $a_{8}=0.0018310546875$ The $8^{\text{th}}$ term is $0.0018310546875$.