Question

In an AP,
Given $a=5,d=3,$ $a_n$ $=50$, find $n$ and $S_n$.

• A. $330$
• B. $390$
• C. $440$
• D. $560$

Answer 1

Answer: (C)

$440$

As we know nth term, $a_n=a+(n-1)d$

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

Given, $a=5,d=3,a_n=50$
$\Rightarrow a+(n-1)d=50$
$\Rightarrow 5+(n-1)3=50$
$\Rightarrow 5+3n-3=50\Rightarrow 3n=48\Rightarrow n=16$
$\therefore S_{16}=\frac{16}{2}[2a+(16-1\left)d\right]=8[2\times 5+15\times 3]=440$
Hence, $n=16,S_{16}=440$