Question

The sum of the series$a-(a+d)+(a+2d)-(a+3d)+..............$ up to $50$ terms is

• A. $-50d$
• B. $25d$
• C. $a+50d$
• D. $-25d$

Answer 1

The correct option is D

$-25d$

Explanation for correct option

Given:$a-(a+d)+(a+2d)-(a+3d)+..............$

$$\begin{gathered} \Rightarrow a-(a+d)+(a+2d)-(a+3d)+.............. \\ \Rightarrow a-a-d+a+2d-a-3d+........... \\ \Rightarrow (a-a)+(a-a)+.........+(2d-d)+(4d-3d)+(6d-5d)+.........(48d-47d)-49d \end{gathered}$$

$\Rightarrow d+d+d+..........$ upto $25$ terms$-49d$

$$\begin{gathered} \Rightarrow 24d-49d \\ \Rightarrow -25d \end{gathered}$$

Hence, $\mathrm{Option}\left(\mathrm{D}\right)$ is correct.