Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 815: 56b

$S_{n}=(3x) \dfrac{1-16x^8}{1-2x^2}$

Here, we have a common ratio $r=x$ and $a_1= 1$ We are given that $S_5= (3x) \sum_{i=1}^4 (2x)^{2i-2}$ We know that $S_{n}=a_1(\dfrac{r^{n}-1}{r-1})$ Hence, $S_{n}=(3x) \dfrac{1-16x^8}{1-2x^2}$