Which is the recursive formula for the nth term in a geometric sequence?

Answer 1

You need to know two numbers to completely describe the geometric sequence: the starting number, and the ratio between each number and the previous one.

When you use recursion, you always need a "base case", otherwise, the recursion will repeat without end.

In words, if "n" is 1, the result is the starting term. Otherwise, it is the ratio times the "n-1"th term.

The following version is appropriate for a programming language (written here in pseudocode, i.e., not for a specific language):

function geometric(starting_number, ratio, term)

if term = 1:

result = starting_number

else:

result = ratio * geometric(starting_number, ratio, term - 1)