Mathematics - Sequence & Series Question with Solution | TestHub

$\begin{array}{rl}& a_1{a}_5=28\Rightarrow a^2{r}^4=28\\ & a_2+a_4=29\Rightarrow ar+a{r}^3=29\end{array}$ ar and $a{r}^3$ are roots of $\begin{array}{rl}& k^2-29k+28=0\\ & \Rightarrow k=1,k=28\\ & ar=1,a{r}^3=28\\ & r^2=28,a^2=\frac{1}{28}\\ & a_6=a{r}^5\Rightarrow r^4=28^2\\ & \Rightarrow a_6=784\end{array}$