Q22 of 36 Page 161

Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n : Sn is equal to

Given that: Sn denote the sum of first n terms

and S2n = 3Sn


To find: S3n : Sn


Now, we know that




⇒ S2n = n[2a + (2n – 1)d]


As per the given condition of the question, we have


S2n = 3Sn




⇒ 4an + 2nd(2n – 1) = 6an + 3nd(n – 1)


⇒ 2nd(2n – 1) – 3nd(n – 1) = 6an – 4an


⇒ 4n2d – 2nd – 3n2d + 3nd = 2an


⇒ nd + n2d = 2an


⇒ nd(1 + n) = 2an


⇒ d(n + 1) = 2a …(i)


Now, we have to find S3n:Sn


So,



[from (i)]





Hence, the correct option is (b)

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