Nth term help?

Question

4, 7, 3, 4,…

in the sequence the first term is 4 & the second term is 7, and each term after the second one is the non-negative difference between the previous 2 terms. If the nth term is the first term of the sequence that is equal to zero, what is the value of n?

Answer

4, 7, 3, 4…

Consider, A(k) = | A(k-1) – A(k-2) | for all k >= 2 with A(0) = 4 and A(1) = 7.

So if A(n) = 0 means that,
A(n-1) = A(n-2).

Its difficult to generate a “formula”…
Thus just consider a few next terms,

4,7,3,4, 1, 3, 2, 1, 1, 0

Count to see that n = 10