Question

Find the sum of first $123$ even natural numbers.

Answer 1

The given sequence is $2,4,6,\mathrm{8...}$

First term $\left(a\right)=2$

Common difference $\left(d\right)=2$

Number of terms $\left(n\right)=123$

We know that,

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

$\therefore S_{123}=\frac{123}{2}\left(2\right(2)+(123-1\left)\right(2\left)\right)$

$=\frac{123}{2}(4+122(2\left)\right)$

$=\frac{123}{2}(4+244)$

$=\frac{123}{2}\times 248$

$=15252$

Hence, the sum of first $123$ even natural number is $15252$.