Question

The sum of all odd numbers between 100 and 200 is
(a) 3750
(b) 2352
(c) 2450
(d) 2468

Answer 1

(d) 7500

All odd numbers between 100 and 500 are 101, 103, 105, ..., 199.
This is an AP in which a = 101, d = (103 - 101) = 2 and l = 199.

Let the number of terms be n.
Then, T_n = 199
⇒ a + (n-1) d = 199

⇒ 101 + (n - 1​) ⨯​ 2 = 199
⇒ 2n = 100
⇒ n = 50

∴ Required sum =$\frac{n}{2}\left(a+l\right)$
$=\frac{50}{2}\left(101+199\right)=25\times 300=7500$
Hence, the required sum is 7500.