Answer:

The series is 101, 103, 105, …, 199

Number of terms be n

a = 101, d = 103 – 101 = 2, a_n = 199

a_n = a + (n-1)d

199 = 101 + (n-1)2

199 = 101 + 2n – 2

2n = 199 – 101 + 2

2n = 100

n = 100/2

n = 50

By using the formula,

The sum of n terms = S

S = n/2[a + l]

S = 50/2 [101 + 199]

S = 25 [300]

S = 7500

∴ The sum of the odd numbers between 100 and 200 is 7500.