Chapter 11.5, Problem 1OE

To determine

To calculate:

Value of $S_5$ for given series.

Answer to Problem 1OE

Value $S_5$ for given series is $27.2$ .

Explanation of Solution

Give information:

  $8+12+16+20$

Calculation:

Given series is,

  $8+12+16+20$

For finding $S_5$ formula used is ,

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

Where,

  $S_n=$ Partial sum.

  $a_1=$ First term.

  $r=$ common ratio.

Initially find out common ratio,

  $\begin{array}{l}r=\frac{a_2}{a_1}\\ r=\frac{-12}{8}\\ r=-1.5\end{array}$

To find $S_5$ ,

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

Substitute the values,

  $\begin{array}{l}{S}_5=8\left(\frac{1-{\left(-1.5\right)}^5}{1-\left(-1.5\right)}\right)\\ S_5=8\left(\frac{1-\left(-7.5\right)}{1+1.5}\right)\\ S_5=8\left(\frac{8.5}{2.5}\right)\\ S_5=8\left(3.4\right)\\ S_5=27.2\end{array}$

Therefore, value $S_5$ for given series is $27.2$ .