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If S(k) denotes the sum of first k terms...

If `S_(k)` denotes the sum of first k terms of a G.P. Then, `S_(n),S_(2n)-S_(n),S_(3n)-S_(2n)` are in

A

A.P.

B

G.P.

C

H.P.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let a be the first term and r be the common ratio of the G.P. Then,
`S_(n)=a((r^(n)-1)/(r-1)),S_(2n)=a((r^(2n)-1)/(r-1))andS_(3n)=a((r^(3n)-1)/(r-1))`
`:." "S_(2n)-S_(n)=ar^(n)((r^(n)-1))/(r-1)andS_(3n)-S_(2n)=ar^(2n)((r^(2)-1)/(r-1))`
`rArr" "S_(2n)-S_(n)=r^(n)S_(n)andS_(3n)-S_(2n)=r^(2n)S_(n)`
`rArr" "S_(n),S_(2n)-S_(n)andS_(3n)-S_(2n)` are in G.P.
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