Question

The mean of the first n terms of the A.P. (a + d) + (a + 3d) + (a + 5d) + .... is

• A. $a + \frac{n}{2} d$
• B. $a + nd$
• C. $a + n^2 d$
• D. none of these

Answer 1

Answer: (B)

$a + nd$

Answer 2

Required A.M. $= \frac{1}{n} \left[\left(a+ d\right) +\left(a+ 3d\right) +\left(a+ 5d\right) +..\text{upto}\, n\, \text{terms}\right]$ = \frac{1}{n} \times\frac{n}{2}\left\\{2\left(a+d\right) + \left(n-1\right)\left(2d\right)\right\\} = \frac{1}{2}\left\\{2a+2d+2nd -2d\right\\} = a+nd.