# Find the sum of the first 100 natural numbers.

Last updated date: 28th Mar 2023

•

Total views: 211.6k

•

Views today: 2.88k

Answer

Verified

211.6k+ views

Hint: Use the formula ${S_{100}} = \dfrac{n}{2}[2a + (n - 1)d]$.

Complete step-by-step answer:

We have to find sum of first 100 natural numbers

Therefore , the natural numbers are 1,2,3,4,5……………..100.

Now ,if we see they form an A.P. with first term (a)=1 and common difference(d)=1 and number of terms(n) =100

Now using the formula of sum given below:

$

{S_{100}} = \dfrac{n}{2}[2a + (n - 1)d] \\

{\text{substituting the values}}{\text{. we get}} \\

{{\text{S}}_{100}} = \dfrac{{100}}{2}[2 \times 1 + (100 - 1) \times 1] \\

{S_{100}} = 50[2 + 99] \\

{S_{100}} = 50 \times 101 \\

{S_{100}} = 5050 \\

\therefore {\text{ The sum of first 100 natural numbers is 5050}}{\text{. }} \\

$

Note: Alternative solution

$

a = 1,d = 1,n = 100 \\

{\text{last term(l)}} = 100 \\

{S_{100}} = \dfrac{n}{2}[a + l] \\

{S_{100}} = \dfrac{{100}}{2}[1 + 100] \\

{S_{100}} = 50 \times [101] \\

{S_{100}} = 5050 \\

$

Complete step-by-step answer:

We have to find sum of first 100 natural numbers

Therefore , the natural numbers are 1,2,3,4,5……………..100.

Now ,if we see they form an A.P. with first term (a)=1 and common difference(d)=1 and number of terms(n) =100

Now using the formula of sum given below:

$

{S_{100}} = \dfrac{n}{2}[2a + (n - 1)d] \\

{\text{substituting the values}}{\text{. we get}} \\

{{\text{S}}_{100}} = \dfrac{{100}}{2}[2 \times 1 + (100 - 1) \times 1] \\

{S_{100}} = 50[2 + 99] \\

{S_{100}} = 50 \times 101 \\

{S_{100}} = 5050 \\

\therefore {\text{ The sum of first 100 natural numbers is 5050}}{\text{. }} \\

$

Note: Alternative solution

$

a = 1,d = 1,n = 100 \\

{\text{last term(l)}} = 100 \\

{S_{100}} = \dfrac{n}{2}[a + l] \\

{S_{100}} = \dfrac{{100}}{2}[1 + 100] \\

{S_{100}} = 50 \times [101] \\

{S_{100}} = 5050 \\

$

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE