Q27 of 78 Page 944

If the sum of first n, 2n and 3n term of an AP be S1 , S2 and S3 respectively, then prove that S3 = 3 (S2 – S1).

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


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