Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises - Page 615: 48

$a_8$

$a_2=ar=30$ $a_5=ar^{4}=3750$ $\frac{a_5}{a_2}=\frac{3750}{30}$ $\frac{ar}{ar^4}=125$ $r^3=125$ $r=\sqrt[3] {125}=5$ $a_n=ar^{n-1}=a(5^{n-1})$ $\frac{a_n}{a_2}=\frac{468,750}{30}$ $\frac{a(5^{n-1})}{a(5)}=15625$ $5^{n-2}=5^6$ $n-2=6$ $n=8$