Find the sum of first 123 even natural numbers. - Vidyadip

Question

Find the sum of first 123 even natural numbers.

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Answer

List of first 123 even natural number is
$2,4,6, \ldots \ldots$
Where first term $a =2$
Second term $t _1=4$
Third term $t _2=6$
Thus, common difference $d=t_2-t_1=6-4=2$
$n=123$
By using sum of $n^{\text {th }}$ term of an A.P. is
$S_n=\frac{n}{2}[2 a+(n-1) d]$
Where, $n=$ no. of terms
$a =$ first term
$d =$ common difference
$S_n=$ sum of $n$ terms
Thus, Substituting given value in formula we can find the value of $S_n$
$\begin{array}{l}
\Rightarrow S_n=\frac{123}{2}[2 \times 2+(123-1) \times 2] \\
\Rightarrow S_n=\frac{123}{2}[4+122 \times 2] \\
\Rightarrow S_n=\frac{123}{2}[4+244] \\
\Rightarrow S_n=\frac{123}{2} \times 248=123 \times 122=15252
\end{array}$
Thus, $S_n=15252$

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