Question

In the arithmetic series, find the sum of the first $n$ terms if the first term is $-11$, the common difference is $4$ and the $n^{th}$ term is $137.$

• A. $1394$
• B. $2394$
• C. $3394$
• D. $4394$

Answer 1

Answer: (B)

$2394$

First term: $a=-11$
Last term, $l=137$
$d=4$

$a_n=a+(n-1)d$
$137=-11+(n-1)4$
$137+11+4=4n$
$152=4n$
$n=38$

$S_n=\frac{n}{2}[a+l]$
$S_{38}=\frac{38}{2}[-11+137]$

$S_{38}=19\left[126\right]$

$S_{38}=2394$