The first term of an A.P. is 5, the last term is 45 and the sum of its term is 1000. Find the number of terms and the common difference of the A.P.

Given, a = 5, l = 45 and S = 1000. Given, l = a 40 = 45 ⇒ a + (40 - 1)d = 45 ⇒ 5 + 39d = 45 ⇒ 39d = 40 ⇒ d = . Hence, n = 40 and d = .

Find the sum of first 51 terms of an A.P. whose 2^nd and 3^rd terms are 14 and 18 respectively.