If a is the first term of a G.P.,l is the n^{ | vedclass

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(A) Let $r$ be the common ratio of the $G.P.$The $n^{th}$ term is given by $l = ar^{n-1} \dots (1)$The first $n$ terms of the $G.P.$ are $a, ar, ar^2,

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$(al)^{n/2}$

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(A) Let $r$ be the common ratio of the $G.P.$The $n^{th}$ term is given by $l = ar^{n-1} \dots (1)$The first $n$ terms of the $G.P.$ are $a, ar, ar^2, \dots, ar^{n-1}$.The product $P$ is given by $P = a 	imes (ar) 	imes (ar^2) 	imes \dots 	imes (ar^{n-1})$.$P = a^n 	imes r^{1+2+3+\dots+(n-1)}$.Using the sum of the first $(n-1)$ natural numbers,$\sum_{k=1}^{n-1} k = \frac{(n-1)n}{2}$.$P = a^n 	imes r^{\frac{n(n-1)}{2}} = (a^2 	imes r^{n-1})^{n/2}$.Since $l = ar^{n-1}$,we can write $a^2 r^{n-1} = a(ar^{n-1}) = al$.Therefore,$P = (al)^{n/2}$.

If $a$ is the first term of a $G.P.$,$l$ is the $n^{th}$ term,and $P$ is the product of the first $n$ terms,then $P=$

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