If the first term of a G.P. is 1 and the sum of $3^{ ext {rd }}$ and $5^{ ext {th }}$ terms is 90

Question

If the first term of a G.P. is 1 and the sum of $3^{	ext {rd }}$ and $5^{	ext {th }}$ terms is 90 , then the positive common ratio of the G.P. is\

Professor PC Thomas Classes · Answer

Let $r$ be the common ratio of the G.P. According to question, we have, $$ \begin{array}{rlr} & a r^{2}+a r^{4}=90 \ \Rightarrow & r^{2}+r^{4}=90 \ \Rightarrow & r^{4}+r^{2}-90=0 \ \Rightarrow & r^{4}+10 r^{2}-9 r^{2}-90=0 \ \Rightarrow & \left(r^{2}+10ight)\left(r^{2}-9ight)=0 \ \Rightarrow & r^{2}=9 \ \Rightarrow & r= \pm 3 \end{array} \quad(\because a=1 	ext { (Given)) } $$