Question

The sum of first $n$ natural number is

• A. $n\left(n-1\right)$
• B. $\frac{n\left(n-1\right)}{2}$
• C. $n\left(n+1\right)$
• D. $\frac{n\left(n+1\right)}{2}$

Answer 1

The correct option is D

$\frac{n\left(n+1\right)}{2}$

Explanation for correct option

The first term of the natural number is $a_1=1$

The second term of the natural number is $a_2=2$

The common difference is $d=1$

Total number of terms $=n$

We know that the sum of A.P is $=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

Therefore the sum of the first $n$ natural number is

$$\begin{gathered} S_n=\frac{n}{2}\left(2·1+1·\left(n-1\right)\right) \\ =\frac{n\left(n+1\right)}{2} \end{gathered}$$

Hence, option D is correct.