Question

If 'p' is the product of n terms in G.P. of which 'a' is the firs and 'l' is the last term, prove that:

Answer 1

To prove:
\[p = (al)^{\frac{ n }{ 2 }}\]

Answer 2

@ganeshie8 @ikram002p

Answer 3

\(a_i = ar^{i-1}\)

\(\begin{align}\Pi a_i &= a^n\left[r^{0+1+2+\cdots+(n-1)}\right] \\~\\&= a^n r^{n(n-1)/2}\\~\\
&= (a^2)^{n/2}\left(r^{n-1}\right)^{n/2}\\~\\
&= \left(a^2r^{n-1}\right)^{n/2}\\~\\
&= \cdots
\end{align} \)