If the first term of a G.P. is 3 and the sum of second and third terms is 60 , then the common ratio

Question

If the first term of a G.P. is 3 and the sum of second and third terms is 60 , then the common ratio of the G.P. is\

Professor PC Thomas Classes · Answer

Let $a$ be the first term and $r$ be the common ratio. Then, $a=3$\ According to question, we have $a_{2}+a_{3}=60$\ $\Rightarrow a r+a r^{2}=60 \Rightarrow 3\left(r+r^{2}ight)=60 \Rightarrow r+r^{2}-20=0$\ $\Rightarrow r^{2}+5 r-4 r-20=0$\ $\Rightarrow(r+5)(r-4)=0 \Rightarrow r=-5$ or 4\