Explanation:

nth  term of a G.P. =tn=a.rn−1
Given: 1st term =1 and sum of 3rd and 5th=90
⇒a=1andt3+t5=90
We know that nth term of a G.P. is tn=a.rn−1
⇒t3=a.r2−1=1×r2=r2 and
t5=a.r5−1=1×r4=r4.
∴r2+r4=90
Let r2=x
then x+x2=90
⇒x2+x−90=0
⇒x2+10x−9x−90=0
⇒x(x+10)−9(x+10)=0
⇒(x−9)(x+10)=0
⇒x=−10orx=9
But since r2 cannot be negative, x=r2=9
⇒r=±3
i.e., The common ratio =±3