Explanation:

The odd numbers between 100 and 200 are
101, 103, 105, …….199
This series is similar to an arithmetic progression, where
The first number in the series, a = 101
Common difference d = second term - first term  = 103 - 101 =2


199 = 101 + (n-1) 2
199 = 101 + 2n - 2
199 = 99 + 2n
2n = 100
n = 50,  
The number of odd numbers between 100 and 200 are 50.

=[2(101)+(50-1)2]
= [202+(49x2)]
=[202+98]
=[