The mean of the series a,a+d,a+2d,…,a+2nd, is

# The mean of the series $a,a+d,a+2d,\dots ,a+2nd,$ is

1. A

$a+\left(n-1\right)d$

2. B

$a+nd$

3. C

$a+\left(n+1\right)d$

4. D

none of these

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### Solution:

We have

Required mean $=\frac{a+\left(a+d\right)+\left(a+2d\right)+\dots +\left(a+2nd\right)}{2n+1}$

$=\frac{\frac{2n+1}{2}\left\{2a+\left(2n+1-1\right)d\right\}}{2n+1}=a+nd$

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