Question

Find the sum of the first 'n' natural numbers and hence find the sum of first 20 natural numbers.

Answer 1

The first n natural numbers are 1, 2, 3,…, n.
We can observe that the numbers are in an A.P.
Here,
First term, a = 1
Common difference, d = t₂ – t₁ = 2 – 1 = 1
We know that the sum of n terms of an A.P. is $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$.
Thus, we have the sum of the first n natural number as:
$$\begin{gathered} S_n=\frac{n}{2}\left[2\left(1\right)+(n-1)\left(1\right)\right] \\ =\frac{n}{2}\left[2+n-1\right] \\ =\frac{n(n+1)}{2} \end{gathered}$$

Now, to find the sum of the first 20 natural numbers, we need to take n = 20.
Thus, we have:

$S_{20}=\frac{20\times 21}{2}=210$