Let a₁, a₂, a₃ ..... be a G.P. of increasing positive terms. If a₁ a₅ = 28 and a₂ + a₄ = 29, the a₆ is equal to

Consider a geometric progression with first term $a$ and common ratio $r$.

Given that $a_1{a}_5=28\Rightarrow a^2{r}^4=28$

It implies that $a{r}^2=\sqrt{28}$

Given that $a_2+a_4=29\Rightarrow ar\left(1+r^2\right)=29$

Dividing the above equations, we get $r+\frac{1}{r}=\frac{29}{\sqrt{28}}\Rightarrow r=\sqrt{28}$ and $a=\frac{1}{\sqrt{28}}$

Therefore, $a_6=\frac{1}{\sqrt{28}}\left(\sqrt{28}\right){\left(28\right)}^2=784$