Question

The arithmetic mean of data with observations $a, a+d, a+2 d, \ldots, a+2 m d$, is

(a) $a+m d$

(b) $a+(m-1) d$

(c) $a+\frac{1}{2} m d$

(d) $a+\frac{1}{2}(m+1) d$

Answer 1

$S=a+(a+d)+(a+2 d)+\ldots+(a+2 m d)$

$=\frac{2 m+1}{2}[2 a+2 m d]$

$=(2 m+1)(a+m d)$

Therefore, Required arithmetic mean $=\frac{(2 m+1)(a+m d)}{(2 m+1)}$

$=(a+m d)$

So, The correct option of this question will be (A).