Given: The first term of a GP is 1 and the sum of its third term and fifth term is 90. Here, a = 1 and let common difference be r. As we know that, the general term of a GP is given by: an=arn−1 ⇒a3=a.r2=r2........(∵a=1) ⇒a5=a.r4=r4........(∵a=1) ∵ The sum of its third term and fifth term is 90 ⇒r2+r4=90 ⇒r4+r2−90=0 Let r2=t, then above equation can be written as: ⇒t2+t−90=0 ⇒t=9 or -10 ⇒r2=9 or -10 ⇒r2=9.......(∵r2≠−10) ⇒ r = ± 3 Hence, the common ratio of the given GP is 3 or - 3.