Question

The $4^{\text{th}}$ and $9^{\text{th}}$ terms of an AP are 18 and 68 respectively. The sum of the first 10 terms of the AP is .

• A. -310
• B. 330
• C. 165

Answer 1

The correct option is B 330

The $n^{\text{th}}$ term of an arithmetic progression is given by
$a_n=a+(n-1)d,$
where $a$ is the first term and
$d$ is the common difference of the AP.

Given,
$a_4=18$ and $a_9=68.$
$\Rightarrow a+(4-1)d=a+3d=\mathrm{18...}\left(1\right)$
$a+(9-1)d=a+8d=\mathrm{68....}\left(2\right)$
Solving (1) and (2), we get $d=10$ and $a=-12.$

The sum of $n$ terms of the AP is given by $S_n=\frac{n}{2}[2a+(n-1\left)d\right].$

The sum of the AP upto 10 terms = $S_{10}$
$\Rightarrow S_{10}=\frac{10}{2}\left(2\right(-12)+(10-1\left)10\right)$
$=5(-24+90)=330$