Question

What is the sum of an odd numbers between 1 to 50?

Answer 1

The odd numbers between 1 to 50 are

3, 5, 7, ......, 49

The above sequence is an A.P.

∴ a = 3, d = 5 – 3 = 2

Let the number of terms in the A.P. be n.

Then, t_n = 49

Since t_n = a + (n – 1)d,

49 = 3 + (n – 1)(2)

∴ 49 = 3 + 2n – 2

∴ 49 = 1 + 2n

∴ 48 = 2n

∴ n =`48/2` = 24

Now, S_n = `"n"/2 ("t"_1 + "t"_"n")`

∴ S₂₄ = `24/2 (3 + 49)`

= 12(52)

= 624

∴ The sum of odd numbers between 1 to 50 is 624.