The period of the function y=sin(1/4 x) is equal to
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Based on these first few terms, we can deduce that the next term is computed by switching the sign of the previous one, and multiplying it by 3: we start with -1, we switch the sign (1) and multiply by 3 (3); then again we switch the sign (-3) and multiply by 3 (-9), and so on.
Since switching sign is the same as multiplying by -1, we can compute every next term by multiplying the previous one by -3:
So, the recursive formula is
because it states precisely that the next term is -3 times the previous one.