Question

If an A. P., $T_{35}=-50$ and $d=-3$ then $S_{35}=$

• A. $35$
• B. $38$
• C. $32$
• D. $29$

Answer 1

The correct option is A

$35$

Explanation for the correct option:

Find the value of $S_{35}$:

Given, $T_{35}=-50,d=-3$

$\Rightarrow$ $a+34d=-50$

$\Rightarrow$$a+34\times -3=-50$

$\Rightarrow$ $a-102=-50$

$\Rightarrow$ $a=-50+102$

$\Rightarrow$ $a=52$

$\begin{array}{rcl}\therefore S_{35}& =& \left(\frac{35}{2}\right)(2\times 52+34\times -3)\\ & =& \mathbf{35}\end{array}$ $\left[\mathbf{\because }{\mathit{S}}_{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}}{\mathbf{2}}\mathbf{(}\mathbf{2}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\mathbf{(}\mathit{n}\mathbf{}\mathbf{-}\mathbf{}\mathbf{1}\mathbf{\left)}\mathit{d}\mathbf{\right)}\right]$

Hence, Option ‘A’ is Correct.