Chapter 11, Problem 9CR

To determine

To calculate: The correct option which shows sum of the following arithmetic series ${\displaystyle \sum _{n=1}^{25}\left(3n+2\right)}$

  $\begin{array}{l}a.984\\ b.1000\\ c.1025\\ d.2050\end{array}$

Answer to Problem 9CR

The correct option is (c).

The sum of the following arithmetic series ${\displaystyle \sum _{n=1}^{25}\left(3n+2\right)}$ is $1025$ .

Explanation of Solution

Given information:

  ${\displaystyle \sum _{n=1}^{25}\left(3n+2\right)}$

Formula used:

Sum of arithmetic series: $S_n=\frac{n\left(a_1+a_n\right)}{2}$

Calculation:

Consider the following sequence:

  $\begin{array}{l}{a}_1=3\left(1\right)+2=5\\ a_{25}=3\left(25\right)+2=77\end{array}$

The sum of the given arithmetic series

  $\begin{array}{l}{S}_n=\frac{n\left(a_1+a_n\right)}{2}\\ S_{25}=\frac{25\left(5+77\right)}{2}\\ S_{25}=1025\end{array}$

The correct option is (c).

The sum of the following arithmetic series ${\displaystyle \sum _{n=1}^{25}\left(3n+2\right)}$ is $1025$ .