Chapter 8.3, Problem 53E

To determine

Find sum of first 8 terms of geometric sequence.

Answer to Problem 53E

Sum of the first 8 term of geometric sequence is $\boxed{S_8=-262140}$

Explanation of Solution

Given information:

Geometric series:

  $-12,-48,-192,-\mathrm{768.....}$

Formula used:

Sum of n term formula of a GP series $S_n=\frac{a_1\left(1-r^n\right)}{1-r}$

First term of the sequence is $a_1=-12$

Find common ratio:

  $\begin{array}{l}r=\frac{a_2}{a_1}=\frac{-48}{-12}\\ \\ r=4\end{array}$

Now finding sum of first 8 terms using formula $S_n=\frac{a_1\left(1-r^n\right)}{1-r}$:

  $\begin{array}{l}{S}_8=\frac{-12\left(1-{\left(4\right)}^8\right)}{1-4}\\ \\ S_8=\frac{-12\left(1-65536\right)}{-3}\\ \\ S_8=4\left(-65535\right)\\ \\ \boxed{S_8=-262140}\end{array}$