The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

Given that, first term = a = 5

Last term = l = 45

To find: common difference (d)

We know that sum of n terms of an AP = n (a + l)/2.

But given, sum of all terms = 400

∴ n (a + l)/2 = 400

⇒ n (5 + 45)/2 = 400

⇒ n (50)/2 = 400

⇒ 25n = 400

⇒ n = 400/25

⇒ n = 16 … (1)

We know that l = a + (n – 1) d.

Substituting the given values and n from (1), we get

45 = 5 + (16 – 1) d

⇒ 45 = 5 + 15d

⇒ 45 – 5 = 15d

⇒ 40 = 15d

⇒ d = 40/15

⇒ d = 8/3

Ans. The common difference d is 8/3.