Question

Find the sum of odd integer from 1 to 100​

Answer 1

The sum of odd integers from 1 to 100 are - 1 + 3 + 5 + 7 + ……… + 99.

This is an Arithmetic Progression with the following parameters:

First Number, a = 1

Last Number, l = 99

Common Difference, d = 2

So, the Number of terms in the Arithmetic Progression, n = (l - a)/d + 1

= (99 - 1)/2 + 1

= 98/2 + 1

= 49 + 1 = 50

So, the sum of the Arithmetic Progression, S = n/2(l + a)

= 50/2(99 + 1)

= 25 X 100

= 2500

So, the sum of odd integers from 1 to 100 = 2500

Answer 2

Given:

Odd integers - 1 to 100

To Find:

Sum of odd integers from 1 to 100

Solution:

The sum of odd integers will be - 1 + 3 + 5 + 7 + __ + 99.

where,

First term, = a = 1  

Last term = l = 99

Common difference = d = 2

AP formula = n = (l - a)/d + 1

Substituting the values -  

= (99 - 1)/2 + 1

= 98/2 + 1

= 49 + 1

= 50

Now,

Sum AP - S = n/2(l + a)

Substituting the values -

= 50/2(99 + 1)

= 50/2(100)

= 2500

Answer: The sum of odd integers from 1 to 100 is 2500