Let a_1, a_2, a_3 ldots. be a G.P. of increas | vedclass

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Question

$a_1 \cdot a_5=28 \Rightarrow a \cdot a r^4=28 \Rightarrow a^2 r^4=28.....(1) $
$a_2+a_4=29 \Rightarrow a r+a r^3=29 $
$\Rightarrow \operatorna

Vedclass · Accepted Answer

$784$

Vedclass · Answer

$a_1 \cdot a_5=28 \Rightarrow a \cdot a r^4=28 \Rightarrow a^2 r^4=28.....(1) $
$a_2+a_4=29 \Rightarrow a r+a r^3=29 $
$\Rightarrow \operatorname{ar}\left(1+r^2ight)=29 $
$\Rightarrow a^2 r^2\left(1+r^2ight)^2=(29)^2......(2)$
By Eq. $(1) \& (2)$
$\frac{r^2}{\left(1+r^2ight)^2}=\frac{28}{29 	imes 29} $
$\Rightarrow \frac{r}{1+r^2}=\frac{\sqrt{28}}{29} \Rightarrow r=\sqrt{28} $
$\because a^2 r^4=28 \Rightarrow a^2 	imes(28)^2=28 $
$\Rightarrow a=\frac{1}{\sqrt{28}} $
$	herefore a_6=a r^5=\frac{1}{\sqrt{28}} 	imes(28)^2 \sqrt{28}=784$

Let $a_1, a_2, a_3 \ldots$. be a $G.P.$ of increasing positive terms. If $a_1 a_5=28$ and $a_2+a_4=29$, then $a_6$ is equal to

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