# create a sequence symbolically and then find a series based on this sequence

I would like to create an infinite sequence (a_o,a_1,a_2,...) symbolically and then find an infinite series sum(a_0+a_1*z+a_2*z+...) based on this sequence with the coefficients based n the initial symbolical sequence. After that I would like to manipulate this sequence further.
I am rather new to Sagemath. How can this be done?
Thanks