Question -
Answer -
The series is 101,103, 105, …, 199
Let the number ofterms be n
So, a = 101, d = 103 –101 = 2, an = 199
an = a+ (n-1)d
199 = 101 + (n-1)2
199 = 101 + 2n – 2
2n = 199 – 101 + 2
2n = 100
n = 100/2
= 50
By using the formula,
The sum of n terms = S= n/2[a + l]
= 50/2 [101 + 199]
= 25 [300]
= 7500
∴ The sum of the oddnumbers between 100 and 200 is 7500.