Answer : We need to prove that the product of the terms equidistant from the beginning and end is the product of first and last terms in a finite GP.

Let us first consider a finite GP. A, AR, AR2….ARn -1, ARn.

Where n is finite.

Product of first and last terms in the given GP = A.ARn

= A2Rn → (a)

Now, nth term of the GP from the beginning = ARn-1 → (1) Now, starting from the end,

So, the product of nth terms from the beginning and end of the considered GP from (1) and (2) = (ARn-1) (AR)
First term = ARn Last term = A

= A2Rn → (b)

So, from (a) and (b) its proved that the product of the terms equidistant from the beginning and end is the product of first and last terms in a finite GP.