Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 815: 53

$S_{11}=\dfrac{4^{11}+1}{5}=838861$

We know that $S_{n}=a_1(\dfrac{r^{n}-1}{r-1})$ Common ratio $r=-4$ and $a_1= 1$ Now, $S_{11}=1[\dfrac{(-4)^{11}}{-4-1}]$ $S_{11}=\dfrac{(-4)^{11}-1}{-5}$ This gives: $S_{11}=\dfrac{4^{11}+1}{5}$ Hence, $S_{11}=\dfrac{4^{11}+1}{5}=838861$