Chapter 11, Problem 8MCQ

To determine

To find the sun of arithmetic series for which

  $a_1=-12,d=8,n=22$

Answer to Problem 8MCQ

The sun of arithmetic series is 1848.

Explanation of Solution

Given:

  $a_1=-12,d=8,n=22$

Concept Used:

The sum of the first n terms of an arithmetic series use the formula: $s_n=\frac{n\left(a_1+a_n\right)}{2}$ .

Calculation:

In order to find sum of arithmetic series

  $a_1=-12,d=8,n=22$

Here, given that first term is -12 and common difference is 8 and $a_n$ is

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ a_n=-12+\left(22-1\right)8\\ a_n=-12+168\\ a_n=180\end{array}$

The sum of the first n terms of an arithmetic series use the formula: $s_n=\frac{n\left(a_1+a_n\right)}{2}$ .

To find sum of arithmetic series $s_{22}$ , as

  $\begin{array}{c}{s}_n=\frac{n\left(a_1+a_n\right)}{2}\\ s_{22}=\frac{22\left(-12+180\right)}{2}\\ s_{14}=\frac{3696}{2}\\ s_{14}=1848\end{array}$

Thus, the sun of arithmetic series is 1848.