Q. 22

# Let Sn

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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