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if the first term of a gp a1 a2 a3 …. is unity such that 4a2 + 4a3 is lest, then the common ratio of a g.p is

if the first term of a gp a1 a2 a3 …. is unity such that 4a2 + 4a3 is lest, then the common ratio of a g.p is 

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Student
$ a_{2}=ra_{1}$
$ a_{3}=r^{2}a_{1}$
$ y=4a_{2}+5a_{3}=4ra_{1}+5r^{2}a_{1}$

To minimize $ y$, set its derivative equal to $ 0$:

$ 0=4a_{1}+10ra_{1}$

$ \boxed{r=-\frac{2}{5}}$
 
Regards
Arun (AskIITians Forum Expert)
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