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In a GP if the (m+n)th term is p and (m-...

In a `GP` if the `(m+n)th` term is `p` and `(m-n)th` term is `q` then `mth` term is

A

`p((q)/(p))^((m)/(2n))`

B

`sqrt(pq)`

C

`sqrt((p)/(q))`

D

None of these

Text Solution

Verified by Experts

Let a be the first term and r be the common ratio, then
`t_(m+n)=p implies ar^(m+n-1)=p " .....(i)"`
`t_(m-n)=q implies ar^(m-n-1)=q " .....(ii)"` From Eqs. (i) and (ii), we get
`ar^(m+n-1)xxar^(m-n-1)=pxxq`
` implies a^(2)r^(2m-2)=pq implies ar^(m-1)=sqrt(pq)`
` implies t_(m)=sqrt(pq)`
Hence, (b) is the correct answer.
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