A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is

where is the n$-$th term of the sequence, is the common ratio obtained by taking any term in the sequence and dividing it by its preceding term, and is the first term of the sequence. Both should be non$-$zero according to its definition.

Write a recursive function to generate first k terms of a geometric sequence. This function should take $,,$ and as inputs, and output first terms in an array.

If any of the inputs are non$-$numeric, or is not an integer greater than or equal to $1,$ your function should output an empty array, i$.$e$.[].$

You are required to use recursion ONLY to solve this problem. Using loops will cost you $1/3$ of the points even if you solve it correctly.

Hints:

When checking if k is an integer, built$-$in functions like isinteger$()$ cannot determine if k is of integer value correctly if k is a single or double $($it only determines whether k is of "integer types" in Matlab$).$ Therefore, try some other methods. We don't want to do typecasting here either which might change the original value of k$.$ One possible solution is to check if the remainder after division of k by $1$ is $0.$

Your function should always produce an output with any k including k$=1$ when no recursion is needed. Use if$-$else$($if$)$ condtional to include all the edge cases.