If the sum of first n, 2n and 3n term of an AP be S 1 , S 2 and S 3 respectively, then prove that S 3 = 3 (S 2 – S 1 ).

Question

Philoid · Accepted Answer

We know that sum of first n terms of an AP is

Where a is first term and d is common difference

So,

Sum of first 2n terms

Sum of first 3n terms

Now, Taking RHS

RHS = LHS

Hence Proved