Mathematics - Sequence & Series Question with Solution | TestHub

For successive harmonic terms $x,y,z,(x+z)y=2xz$. Apply this at indices $(1,2,3)$ and $(3,4,5)$ : the sum is $2a_3\left(a_1+a_5\right)$. Applying the same identity to $(1,3,5)$ gives $a_3\left(a_1+a_5\right)=2a_1{a}_5$, hence the result is $4a_1{a}_5$.