UPSC NDA Math Model Paper 3

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.