Question

The sum of n, 2n, 3n terms of an ap are S1, S2 and S3 Respectively. Prove that S3 = 3 (S2 - S1)

Answer 1

that's ans because sum of n term is n(n+1)÷2

Answer 2

Sol: Let ‘a’ be the first term of the AP and ‘d’ be the common difference S1 = (n/2)[2a + (n – 1)d] --- (1) S2 = (2n/2)[2a + (2n – 1)d] = n[2a + (n – 1)d] --- (2) S3 = (3n/2)[2a + (3n – 1)d] --- (3) Consider the RHS: 3(S2 – S1) 

refer the picture **Above


 = S3
 = L.H.S ∴ S3 = 3(S2 - S1) .