Chapter 11.5, Problem 15WE

To determine

To calculate:

Sum of given geometric series.

Answer to Problem 15WE

Sum of given geometric series is $29525$ .

Explanation of Solution

Give information:

  $n=10,r=-3,t_1=2$

Calculation:

Given series is,

  $n=10,r=-3,t_1=2$

To find sum of geometric series,

  $S_n=\frac{a_1{\left(1-r\right)}^n}{1-r}$

Where,

  $a_1=$ First term,

  $r=$ Common ratio.

After substituting the values in above equation,

  $\begin{array}{l}{S}_n=\frac{a_1\left(1-r^n\right)}{1-r}\\ S_n=\frac{2\left(1-{\left(-3\right)}^{10}\right)}{1-\left(-3\right)}\\ S_n=\frac{2\left(1-\left(-59049\right)\right)}{4}\\ S_n=\frac{2\left(59050\right)}{4}\\ S_n=\frac{118100}{4}\\ S_n=29525\end{array}$

Therefore, Sum of given geometric series is $29525$ .