Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 815: 40

$a_n=5^{n-1}$

The nth term is given by $a_n= a_1 r^{n-1}$ ...(1) When $n=5$, then we have Equation (1) gives: $a_5=a_1(1.5)^{5-1}=a_1r^4$ Plug in $a_5=625$ and $a_1=1$ $625=(1)r^4$ This gives: $r=5$ Hence, $a_n=5^{n-1}$