Question

Find the sum of first 100 odd natural numbers.​

Answer 1

Step-by-step explanation:

Given:-

First 100 odd natural numbers

To find:-

Find the sum of first 100 odd natural numbers.

Solution:-

Method-1:-

The first 100 odd natural numbers

= 1,3,5,7,...(100 numbers)

First term (a) = 1

Second term = 3

Common difference (d) = 3-1= 2

Common difference = 2

Number of terms (n) = 100

We have the common difference is 2 throughout the series

So 1,3,5,7... are in the A.P.

We know that

The sum of first n terms in the AP

Sn = (n/2)[2a+(n-1)d]

We have

a = 1

d = 2

n = 100

On Substituting these values in the above formula

=>S100 = (100/2)[2(1)+(100-1)(2)]

=>S100 = (50)[2+(99)(2)]

=> S100 = 50(2+198)

=> S100 = 50(200)

=> S100 = 10000

Method -2:-

The sum of first n odd natural numbers = n^2

We have n = 100

Sum of first 100 odd natural numbers

=> (100)^2

=> 100×100

=> 10,000

Answer:-

The Sum of first 100 odd natural numbers = 10,000

Used formulae:-

• The sum of first n terms in the AP
• Sn = (n/2)[2a+(n-1)d]
• The sum of first n odd natural numbers = n^2
• n = number of terms
• a = first term
• d= Common difference