If you take a look at sum of first n odd numbers, you can notice very interesting pattern.

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

1 + 3 + 5 + 7 + 9 + 11 = 36

So, sum of first n odd numbers is equal to . Similarly, Sum of first 25 odd numbers would be equal to .

Using the same concept, can we find sum of (1 + 3 + 5 + 7 + 9 + 11 + ......99).

We know that we have 50 odd numbers from 1 to 100. Therefore, (1 + 3 + 5 + 7 + 9 + 11 + ......99) which is equal to sum of first 50 odd numbers.

**Application:**

Can you find the value of 101+103+105+107+......199 using the same concept? It becomes little tricky here.

We know that 1 + 3 + 5 + 7 + 9 + .... 199 . Here n = 100 because we know that there are 100 odd numbers from 1 and 200. (1 + 3 + 5 + 7 + 9 + .... 199 ) is the sum of first 100 odd numbers.

We also know that 1 + 3 + 5 + 7 + 9 + .... 99

(101+103+105+107+......199) = (1 + 3 + 5 + 7 + 9 + ....199) - (1 + 3 + 5 + 7 + .....99) = 10000 - 2500 = 7500