# What is the Sum of First 100 Odd Numbers?

## How to Find the Sum of First 100 Odd Numbers?

The below workout with step by step calculation shows how to find what is the sum of first 100 odd numbers by applying arithmetic progression. It's one of the easiest methods to quickly find the sum of given number series.

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 1, 3, 5, 7, 9, . . . . , 199.

The first term a = 1

The common difference d = 2

Total number of terms n = 100

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + T_{n})

= 100/2 x (1 + 199)

= (100 x 200)/ 2

= 20000/2

1 + 3 + 5 + 7 + 9 + . . . . + 199 = 10000

Therefore, **10000** is the sum of first 100 odd numbers.

You may like the below resources!