Question

Find the sum of all the odd number within 100

Answer 1

ANSWER: 2500

EXPLANATION :

Step-by-step explanation:

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 = 250

AVERAGE SUM WOULD BE : 50