Question

Let S_n denote the sum of the first n terms of an A.P. If S_2n = 3S_n then S_3n : S_n is equal to

A. 4
B. 6
C. 8
D. 10

Answer 1

Given that: S_n denote the sum of first n terms

and S_2n = 3S_n

To find: S_3n : S_n

Now, we know that

⇒ S_2n = n[2a + (2n – 1)d]

As per the given condition of the question, we have

S_2n = 3S_n

⇒ 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 S_3n:S_n

So,

Hence, the correct option is (b)