Question

Find the sum of the first $30$ natural numbers.

Answer 1

Calculate the sum of the first thirty natural numbers

Positive integer numbers are known as natural numbers.

The first $30$ natural numbers are $1,2,3,....,30$.

It is clear that they are in arithmetic progression.

Thus, the number of terms, $n=30$.

The first term, $a=1$.

The last term, $l=30$.

The sum of the progression, $\mathit{S}\mathbf{=}\frac{\mathbf{n}}{\mathbf{2}}\left(a+l\right)$.

Substituting the respective values,

$\begin{array}{rcl}S& =& \frac{30}{2}\left(1+30\right)\\ & \Rightarrow & S=15\times 31\\ & \Rightarrow & S=465\end{array}$

Therefore, the sum of the first thirty natural numbers is $465$.