This is an arithmetic progression based question from Chapter name- Arithmetic Progression

Chapter number- 9

Exercise – 9.6

In this question we have been given that the sums of first n terms of three A.P.s are S1, S2 and S3.

Also the first term of each is 5 and their common differences are 2, 4 and 6 respectively.

Now we have to prove that S1 + S3 = 2S2

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Understanding CBSE Mathematics

Class :- 10th

Question no 59

By using the formula of the sum of n terms of an A.P.

S

_{n}Â = n[2a +(n â€“ 1)d] / 2According to the question,

S

_{1}Â = n[2(5)+(n â€“ 1)2] / 2 = n[8 + 2n] / 2 = 4n + n^{2}S

_{2}Â = n[2(5) + (n â€“ 1)4] / 2 = n[6 + 4n] / 2 = 3n + 2n^{2}S

_{3}Â = n[2(5) + (n â€“ 1)6] / 2 = n[4 + 6n] / 2 = 2n + 3n^{2}Now, L.H.S. = (4n + n

^{2}) + (2n + 3n^{2})= 6n + 4n

^{2}= 2[3n + 2n

^{2}]= 2S

_{2}Hence proved.