(a_{p+q}=m=ar^{p+q-1}), (a_{p-q}=n=ar^{p-q-1})
[ a_p=ar^{p-1} ]
[ \sqrt{mn}=\sqrt{a^2 r^{2p-2}}=a r^{p-1}=a_p ]
(when (mn>0); in general (a_p=\sqrt{mn}) or (-\sqrt{mn}) depending on signs)
Answer: (a_p=\sqrt{mn}) (taking positive case)
11TH•Mathematics•Sequences And Series•Question 8
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If $(p+q)^{th}$ term of a G.P. is $m$ and $(p-q)^{th}$ term is $n$, then find the $p^{th}$ term.
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