Q54 of 84 Page 5

The sums of first n terms of three arithmetic progressions are S1, S2 and S3 respectively. The first term of each A.P. is 1 and their common differences are 1, 2 and 3 respectively. Prove that S1 + S3 = 2S2. (CBSE 2016)

As we know that sum of An AP, upto first n terms is



Where S = sum of first n terms


a = first term , d = common difference


For first AP a = 1, d = 1




For second AP a = 1 , d = 2




For second AP a = 1 , d = 3




Adding S1 and S3




Hence proved.

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