Find the sum of all odd integers from 1 to 201.

To Find: The sum of all odd integers from 1 to 201.

The odd integers form the following AP series:

1,3,5….201

First term = a = 1

Common difference = d = 2

Last term = 201

Let the number of terms be n

$\Rightarrow 1+2(n-1)=201$

$\Rightarrow n-1=100$

$\Rightarrow n=101$

Sum of AP series $=\frac{n}{2}($ First term $+$ Last term $)$

$=\frac{101}{2}(1+201)$

= 101 × 101 = 10201

The sum of all odd integers from 1 to 201 is 10201.