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Mathematics 7 Online
OpenStudy (crashonce):

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:

OpenStudy (crashonce):

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

OpenStudy (crashonce):

@ganeshie8 @ikram002p

ganeshie8 (ganeshie8):

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

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