The third term of a G.P. is the square of its first term. If its third term is 8,
Question:

The third term of a G.P. is the square of its first term. If its third term is 8, then the common ratio is ____________.

Solution:

Let the G.P be aarar2

According to given condition,

third term = (first term)2

i.e ar2 = a2

i.e r2 = a            (1)

given ar2 = 8   (given)

i.e a2 = 8

i. e $a=\sqrt{8}$