If the first and the nth term of aG.P are a and b, and P is the product of first n terms, prove :

it is as we have inserted (n-2) G.M. between a and b.

r= (b/a)^(n-2+1)= (b/a)^(n-1)

so product of all these terms P= a.ar.ar².ar³........ar^(n-1)

 =aⁿ.r^{(1+2+3+.....(n-1))}

=an.r^(n*(n-1)/2)

put the value of r

P= aⁿ . (b/a)^n/2 = (ab)^n/2

i.e. P²=(ab)^n.