if a G.P (p+q)th term = m and (p-q) th term = n , then find its p th term

Options

A. `(mn)^(1//2)`
B. mn
C. `m + n`
D. `m-n`

Answer

A

Explanation

Since, `T_(p+q)=m=a(r )^(p+q-1) " " `…(i)
`and T_(p-q)=n=a(r )^(p-q-1) " " ` …(ii)
On multiplying Eqs. (i) and (ii), we get
`mn=a^(2)(r )^(2p-2)`
`rArr a(r )^(p-1)=(mn)^(1//2)`
`therefore T_(p)=(mn)^(1//2)`