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

Options

A. `p((q)/(p))^((m)/(2n))`
B. `sqrt(pq)`
C. `sqrt((p)/(q))`
D. None of these

Explanation

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.