Question

The mean of the series $a,a+nd,a+2nd$ is

• A. $a+(n-1)d$
• B. $a+nd$
• C. $a+(n+1)d$
• D. None of these

Answer 1

The correct option is B

$a+nd$

Explanation for the correct option.

Find the mean of the given series.

A series of three terms $a,a+nd,a+2nd$ is given.

We know that, mean $\overline{x}$ is given by $\overline{x}=\frac{{\displaystyle \sum _{i=1}^n}{x}_i}{n}$.

Therefore, the mean of the given series is as follows:

$$\begin{gathered} \overline{x}=\frac{a+a+nd+a+2nd}{3} \\ \Rightarrow \overline{x}=\frac{3a+3nd}{3} \\ \Rightarrow \overline{x}=a+nd \end{gathered}$$

Therefore, the mean of the given series is $a+nd$.

Hence, option $B$ is the correct answer.