If first term of a G.P. a₁, a₂, a₃...... is unity such that 4a₂ + 5a₃ is least, then

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8. Sequences and Series

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If the first term of a $G.P. a_1, a_2, a_3......$ is unity such that $4a_2 + 5a_3$ is least, then the common ratio of $G.P.$ is

A

$-0.4$

B

$-0.6$

C

$0.4$

D

None of these

Solution

$a_{1}=1, a_{2}=r, a_{3}=r^{2}, \ldots \ldots .$

$\therefore 4 \mathrm{a}_{2}+5 \mathrm{a}_{3}=4 \mathrm{r}+5 \mathrm{r}^{2}$

To be its minimum $\frac{d}{d r}\left(4 r+5 r^{2}\right)=0$

$ \Rightarrow r=\frac{-2}{5}$

Standard 11

Mathematics

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