Question

The $n^{th}$ term of an AP is given by $a_n=2+5n$. The sum of the first 10 terms of the AP is .

• A. 290
• B. 330
• C. 350
• D. 295

Answer 1

Answer: (C), (D)

295

The sum of the first $n$ terms of an AP with first term $a$ and common difference $d$ is given by
$S_n=\frac{n}{2}(2a+(n-1\left)d\right).$
Given, $a_n=2+5n.$
$\therefore a_1=7,a_2=12,a_3=\mathrm{17...}\text{and so on.}$
$\therefore a=a_1=7$ and $d=a_2-a_1=5.$
$⟹S_{10}=\frac{10}{2}\left(2\right(7)+(10-1\left)5\right)$
$=5\left(59\right)$
$=295$
Thus, the sum of the first 10 terms of this AP is 295.