Find a formula for tn, the nth term of the series. Then give a recursive definition for Sn, the sum of n terms of the series.

1) 8+12+18+27+....

2) 50+47+44+41+....

I know how to find the tn

tn = tn-1 * (3/2)

tn = 53-3n

My teacher gave us the answers

1. Sn = Sn-1 + 8(3/2)^(n-1)

2. Sn = Sn-1 +53-3n

Can somebody explain to me why these two are the answers for the recursive definition of Sn and how to write one? Thanks!