Let a _1, a _2, a _3, ldots be a G.P. of incr | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$a r^5+a r^7=2$

$\left(a r^2\right)\left(a r^4\right)=\frac{1}{9}$

$a^2 r^6=\frac{1}{9}$

Now, $r > 0$

$\operatorname{ar}^5\left(1+r^2\r

Vedclass · Accepted Answer

$3$

Vedclass · Answer

$a r^5+a r^7=2$

$\left(a r^2\right)\left(a r^4\right)=\frac{1}{9}$

$a^2 r^6=\frac{1}{9}$

Now, $r > 0$

$\operatorname{ar}^5\left(1+r^2\right)=2$

Now, $ar ^3=\frac{1}{3}$ or $-\frac{1}{3}$ (rejected)

$r^2=2$

$r=\sqrt{2}$

$a=\frac{1}{6 \sqrt{2}}$

Now, $6\left(a_2+a_4\right)\left(a_4+a_6\right)$

$6\left(a r+a r^3\right)\left(a r^3+a r^5\right)$

$6 a^2 r^4\left(1+r^2\right)$

$6\left(\frac{1}{36.2}\right)(4)(9)=3$

Similar Questions

The first term of a $G.P.$ is $1 .$ The sum of the third term and fifth term is $90 .$ Find the common ratio of $G.P.$

The number $111..............1$ ($91$ times) is a

If $3 + 3\alpha + 3{\alpha ^2} + .........\infty = \frac{{45}}{8}$, then the value of $\alpha $ will be

If $x,\;y,\;z$ are in $G.P.$ and ${a^x} = {b^y} = {c^z}$, then

if $x = \,\frac{4}{3}\, - \,\frac{{4x}}{9}\, + \,\,\frac{{4{x^2}}}{{27}}\, - \,\,.....\,\infty $ , then $x$ is equal to