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3rd question:
a1, a2, a3, a4, ...................... are in A.P. with common difference d
S1 = n/2 (2a1 + (n - 1)d) = a1n + n2d/2 - dn/2
S2 = (S1 + S2) - S1 = n (2a1 + (2n - 1)d) - S1 = a1n + 3n2d/2 - dn/2
S3 = (S1 + S2 + S3) - (S1 + S2) = a1n + 5n2d/2 - dn/2
Now note that : 2S2 = S1 + S3
S1, S2, S3, .......................................... are in A.P. whose difference is S2 - S1 = S3 - S2 = n2d
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Moderation Team
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