Question

How many consecutive natural numbers starting from 1 can be added to get 5050?

• A. 98
• B. 99
• C. 100
• D. 101

Answer 1

The correct option is C

100

1 + 2 + 3 + 4 + ....+ 5050

Let us assume that the sum of first n natural numbers is 5050. Therefore

$\frac{n(n+1)}{2}=5050$

$n^2+n=10100$

$n^2+n-10100=0$

Using quadratic formula

$n=\frac{-1\pm \sqrt{40400}}{2}$

$n=\frac{-1\pm 201}{2}$

$n$ = 100 or -101

Let's ignore the negative value for number of terms.

$n$ = 100

The sum of first 100 natural numbers will be 5050.