If s1=n ,s2=2n , and s3=3n than prove that s3=3 (s2-s1)

1.	If s1=n ,s2=2n , and s3=3n than prove that s3=3 (s2-s1)
Answer» 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) .

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