Q:

Definition clarification of Geometric Sequences

So I get that the definition of a geometric sequence is {cr^k} = {c,cr,cr^2, cr^3,....} with a starting value at k=0 and an upper bound/end of infinite. Where r is a constant multiplication factor.
My textbook states a geometric sequence {g subscript k} can be defined recursively as  gsub0=c;and for k>=1, g sub k = rg sub(k-1). 
I don't really get this recursive definition, I understand g0=c because its the first term at k=0 so their is no constant of r to multiply it by, but I get lost at the part after. Could someone explain it in words possibly?
Sorry I don't know how to subscript on this site, sub means subscript where written.

A:

The idea is that $g_k = rg_{k-1}$ for $k \ge 1$. So you get for example
$$
g_3 = rg_2 = r(rg_1) = r^2g_1 = r^2(rg_0) = r^3g_0
$$

