Question

The sum of the first ___ natural numbers is 210.

• A. 20
• B. 21
• C. 18
• D. 19

Answer 1

The correct option is A

20

The sum of the first $n$ natural numbers is given by $\frac{n(n+1)}{2}.$

From the given data, $\frac{n(n+1)}{2}=210$

$\Rightarrow n^2+n-420=0$

Using quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here, $a=1,b=1$ and $c=-420$

$\Rightarrow n=\frac{-1\pm \sqrt{(1+1680)}}{2}$

$\Rightarrow n=\frac{-1\pm 41}{2}$

On solving, we get $n=20$ and $-21$.

Since '$n$' represents the number of terms, we ignore the negative value.

Thus, $n=20$, i.e., the sum of the first 20 natural numbers is 210.