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

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

A
$a + (n - 1) d$
B
$a + n d$
C
$a + (n + 1) d$
D
none of these

Solution:

We have

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

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

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