Chapter 11.5, Problem 9WE

To determine

To calculate:

Sum of given arithmetic series.

Answer to Problem 9WE

Sum of given arithmetic series is $120.5$ .

Explanation of Solution

Give information:

  $4+7+10+13$

Calculation:

Given series is,

  $4+7+10+13$

Her, $a_1=4$ and common difference is $d=7-4=3$ last term given is $100$ ,

The $n^{th}$ term is given by,

  $a_n=a_1+\left(n-1\right)d$

Put the values in above equation to get ${100}^{th}$ term,

  $\begin{array}{l}100=4+\left(n-1\right)3\\ 100=3n+1\\ 3n=99\\ n=33\end{array}$

The sum of series is given by,

  $\begin{array}{l}=\frac{n}{2}\left(a_1+a_n\right)\\ =\frac{33}{2}\left(4+100\right)\\ =16.5\left(104\right)\\ =120.5\end{array}$

Therefore, Sum of given arithmetic series is $120.5$ .