In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

The general formula of a gemotric sequnce is: a, ar, ar^2, ar^3, ar^4, ar^5 ..... where r cannot = 0 is the common ratio and "a" is a scale factor equal to the sequences start value.

The n-th term of a geometric sequence with scale factor/initial value "a" and common ratior "r" is given by:

An = Ar^n-1

such a geometic sequence also folows the recursive relation:

An = rA_n-1 (rAsub(n-1)) for every integrer n >= 1

Write a SCHEME fucntioin to compute the n-th term of a geometric dequence given the common ratio, r, and the scale factor, a, using a recursive alogorithm based on this recursive relation. (if you cannot do it in SCHEME language but can do it in either java or c++ RECURSIVELY, that will help as well (i will attempt to translate it))

in lamen terms he wants to be able to give it the scale factor and ratio, and it computes the index n of the term in the sequence starting at 1. so im thinking there has to be a counter somehwere of how many times "recurrsion" happens but if i initilaize that in the same funciton, it'll restart the counter everytime the function is called. so not sure what do here. Not even sure what the base case is considering we're only gvien scale factor and the rator and told to find the index or n-th term