Question

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?

Answer 1

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.