Question

If the sum of first n, 2n and 3n terms of an AP is S¹,S²,S³ respectively then prove that S³ = 3(S²-S¹).​

Answer 1

Answer:

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Step-by-step explanation:

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)

= S3

= L.H.S ∴ S3 = 3(S2 - S1)