Question

Given $d=5,S_9=75$, find a

• A. $\frac{-35}{3}$
• B. $\frac{-28}{3}$
• C. $\frac{-54}{3}$
• D. $\frac{-34}{3}$

Answer 1

Answer: (A)

$\frac{-35}{3}$

We know that sum of first $n$ terms, $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$, where $a$ & $d$ are the first term & common difference of an AP.

$\therefore S_9=\frac{9}{2}(2a+d(9-1\left)\right)$

$\Rightarrow 75=4.5(2a+8d)$
$\Rightarrow 2a+8d=\frac{75}{4.5}$
$\Rightarrow 2a=\frac{150}{9}-40=\frac{150-360}{9}=\frac{-210}{9}=\frac{-70}{3}$
$\Rightarrow a=\frac{-35}{3}$