Question

If sum of n, 2n, 3n terms of any A.P. are S₁, S₂ and S₃ respectively, then prove that S₃ = 3 (S₂ – S₁).

Answer 1

Let a is first term and dis common difference of an A.P. then

Subtracting equation (i) from equation (ii)

​​​​​​Multiplying by 3 in both sides

3(S₂ - S₁) = 3n/2[2a + (3n - 1)d]

= S₃  [From equation (iii)]

Hence, 3 (S₂ – S₁) = S₃

Hence Proved.