Finding the nth term in a repeating number sequence I'm trying to figure out how to solve these types of repeating number sequence problems. Here is one I made up:
Consider the following repeating number sequence: {4, 8, 15, 16, 23, 42, 4, 8, 15, 16, 23, 42, 4, 8, 15, 16, 23, 42,…} in which the first 6 numbers keep repeating. What is the 108th term of the sequence?
I was told that when a group of k numbers repeats itself, to find the *n*th number, divide n by k and take the remainder r. The *r*th term and the *n*th term are always the same.
108 / 6 = 18, r = 0
So the 108th term is equal to the 0th term? Undefined?
I'm confused at how this works.
Thanks!

HINT:
In such cases, look at more manageable sample problems. So what would the 5th, 10th, 12th, 17th element (etc.) be? All these can be found by hand, and you can see how the remainder matters.
