If first term of a G.P. {a₁},{a₂},{a₃},.......... is unity such that 4{a₂} + 5{a₃} is leas

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8. Sequences and Series

hard

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

A

$ - \frac{2}{5}$

B

$ - \frac{3}{5}$

C

$\frac{2}{5}$

D

None of these

Solution

(a) ${a_1} = 1,\;{a_2} = r,\;{a_3} = {r^2},…….$

$\therefore $$4{a_2} + 5{a_3} = 4r + 5{r^2}$

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

$ \Rightarrow $$r = \frac{{ – 2}}{5}$.

Standard 11

Mathematics

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