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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 $4{a_2} + 5{a_3}$ 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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