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Consider a sequence defined by the recursive rule f(1) = 15, f(n) = f(n - 1) - 6. What is the third term of the sequence?

User ScottSto
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According to the problem, the recursive rule is


\begin{gathered} f(1)=15 \\ f(n)=f(n-1)-6 \end{gathered}

This means the first term of the sequence is 15.

So, for n = 2, we have


f(2)=f(2-1)-6=f(1)-6

But, we know that f(1) = 15, so


f(2)=15-6=9

The second term is 9.

For n = 3.


f(3)=f(3-1)-6=f(2)-6

But, we know that f(2)=9, so


f(3)=9-6=3

Therefore, the third term is 3.

User The Reverend
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