Question

# Let $$S_{n}$$ denotes the sum of first $$n$$ terms of an $$A.P$$. If $$S_{2n}=3\ S_{n}$$, then the ratio $$S_{3n}/S_{n}$$ is equal to

A
4
B
6
C
8
D
10

Solution

## The correct option is B $$6$$We know. $$S_n =\dfrac {n(n+1)}{2}$$$$\therefore \ S_{2n} =\dfrac {2n(2n+1)}{2}$$Now, $$S_{2n}=3S_{n}\ \Rightarrow \dfrac {2n(2n+1)}{2}=3\dfrac {n(n+1)}{2}$$or, $$4x+2=3n+3\Rightarrow n=1$$$$\therefore \ \dfrac {S_{3n}}{S_n}=\dfrac {3(1)[3(1)+1]}{2}\times \dfrac {2}{1(1+1)}=\dfrac {3\times 4}{2}=\boxed {6}$$Mathematics

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