Hi

I am gonna give you general proof for this AGP, Arithmetico-Geomtric Series

is an AP and is a GP

The series we have is

Now

........(1)

..........(2)

We now substract (1) -(2)

.................................................. ...............................................

Now you should always remember the way of proof of this thing for any general term and apply as it is in your case

For going further ,when -1< r <1