Question
Find the sum of first n natural numbers.
✓
Answer
First $n$ natural numbers are $1,2,3, \ldots, n$.
Here $a=1, d=1, n^{\text {th }}$ term $=n$
$\begin{aligned}
\therefore & S _{ n }=1+2+3+\ldots+n \\
S _{ n } & =\frac{n}{2}[\text { First term + last term] } \ldots \ldots \text { (by the formula) } \\
& =\frac{n}{2}[1+n] \\
& =\frac{n(n+1)}{2}
\end{aligned}$
$\therefore$ Sum of first $n$ natural number is $\frac{n(n+1)}{2}$.
Here $a=1, d=1, n^{\text {th }}$ term $=n$
$\begin{aligned}
\therefore & S _{ n }=1+2+3+\ldots+n \\
S _{ n } & =\frac{n}{2}[\text { First term + last term] } \ldots \ldots \text { (by the formula) } \\
& =\frac{n}{2}[1+n] \\
& =\frac{n(n+1)}{2}
\end{aligned}$
$\therefore$ Sum of first $n$ natural number is $\frac{n(n+1)}{2}$.
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