What recursive formulas represent the same geometric sequence as the formula?

To represent a geometric sequence recursively, you can use the formula ( a_n = r \cdot a_{n-1} ), where ( r ) is the common ratio and ( a_1 ) is the first term of the sequence. The first term can be defined explicitly, such as ( a_1 = A ), where ( A ) is a constant. This recursive definition effectively captures the relationship between consecutive terms in the sequence.