Question

Find the sum of all even numbers between 5 and 100.

Answer 1

All the even numbers between 5 and 100 are 6, 8, 10, 12,..., 98.

This is an AP in which a = 6, d = (8 - 6) = 2 and l = 98.

Let the number of terms be n.
Then T_n = 98
⇒ a + (n - 1)d = 98
⇒ 6 + ( n - 1​) ⨯​ 2 = 98
⇒ 2n = 94
⇒ n = 47

∴ Required sum = $\frac{n}{2}\left(a+l\right)$
= $\frac{47}{2}\left[6+98\right]=47\times 52=2444$
Hence, the required sum is 2444.