Q) The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.

Ans:

Given that a = 15 and Sum of 15 terms of an A.P.  S₁₅ = 750

We know that sum of n terms of an A.P.  S_n = (2a + (n-1) d)

  S₁₅ = (2 x 15 + (15 – 1) d) = 750

15 (30 + 14 d ) = 750 x 2

30 + 14 d = 100

14 d = 70

d = 5

Next, we know that n^th term of an A.P.  =  a + (n-1) d

Hence,  20^th term, N₂₀ = 15 + (20 – 1) x 5 = 15 + 19 x 5 = 110

Therefore, the value of 20^th terms is 110.