The sum of first n, 2n, and 3n terms of an AP is S1, S2, and S3 respectively. Prove that S3=3(S2−S1).
Answer:
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We are told that
S1 = Sum of first n terms
S2 = Sum of first 2n terms
S3 = Sum of first 3n terms
- We know that the sum of first n terms of an AP is given by
Sn=n2(2a+(n−1)d), where a is the first term and n is the number of terms in the AP.
Therefore, we have - Now,
- Thus,