Question

Enter the first four terms.

Answer 1

7, 4, 1, and -2.

Explanation:

Our recursive rule is:

`f(1)=7\!, f(n)=f(n-1)-3`

Where n is the nth term.

So, our first term will be f(1). As defined, this is 7.

Our second term will be f(2). We will use the recursive formula. Substituting 2 for n yields:

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

Subtract:

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

We know that f(1) is 7. Substitute:

`f(2)=7-3=4`

Hence, the second term is 4.

We will do the same thing for the third term. Substitute 3 for n:

`f(3)=f(3-1)-3`

Subtracting yields:

`f(3)=f(2)-3`

We know that f(2) is 4. So:

`f(3)=4-3=1`

Hence, the third term is 1.

Finally, we will do the same thing. Substitute 4 for n to find the fourth term:

`\begin{aligned} f(4)&=f(4-1)-3 \\ f(4)&=f(3)-3 \\ f(4)&=1-3 \\ f(4)&=-2\end{aligned}`

Hence, the fourth term is -2.

Therefore, our first four terms are 7, 4, 1, and -2.