Question

In an AP ,the sum of 10terms is 150 and sum of next 10 term is 550

Answer 1

The sum of the first n terms of an AP is S_n = (n/2)[2a + (n-1)·d] n = 10, S₁₀ = 150 150 = (10/2)[2a + (10 - 1)d] 150 = 5[2a + 9d] Dividing through by 5, 30 = 2a + 9d ----------(1)

Given sum ofits next 10 terms is - 550.

n = 10, S_n = 550 Here a = a + 10d 550 = (10/2)[2(a + 10d) + (10-1)d] 550 = 5[2a + 29d] Dividing through by 10, 110 = 2a + 29d ----------(2) Solving (1) and (2) we get d = 4 and a = -3.