Question

What is the sum of the first $n$ terms if the first term is $2$, the common difference is $5$ and the $n^{th}$ term is $122$ in an arithmetic series?

• A. $1250$
• B. $1350$
• C. $1450$
• D. $1550$

Answer 1

The correct option is D $1550$

First term: $a=2$
last term, $l=122$
$d=5$

$a_n=a+(n-1)d$
$122=2+(n-1)5$
$122-2+5=5n$
$125=5n$
$n=25$
$S_n=\frac{n}{2}[a+l]$

$S_{25}=\frac{25}{2}[2+122]$

$S_{25}=12.5\left[124\right]$

$S_{25}=1550$