Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

What is the sum of the first $100$ natural numbers?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

- 5050

5005

5050

- 5005

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given the natural numbers 1,2,3……100.
The natural number form an AP with first term 1 and common difference 1.
So, we have,

a = 1, d = 1

.
We know that sum of first n terms of an AP is given as,

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

.
Putting the value of a = 1 and d = 1, we get

\Rightarrow S_{n}

= \frac{n}{2} [2 \times 1 + (n - 1) \times 1]

\Rightarrow S_{n} = \frac{n}{2} [2 + n - 1]

\Rightarrow S_{n} = \frac{n}{2} [n + 1]

\Rightarrow S_{n} = \frac{n (n + 1)}{2}

[1]
Substituting

n = 100

in [1], we get

S_{100} = \frac{100 (100 + 1)}{2}

{\Rightarrow S}_{100} = 50 \times 101

{\Rightarrow S}_{100} = 5050

Therefore, the sum of the first 100 natural numbers is 5050.
Hence, the correct option is 3.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE