Question

h(n)=-13nComplete the recursive formula of
\[h(n)\].
\[h(1)=\]

Answer 1

To express the recursive formula for the sequence defined by \( h(n) = -13n \), we start by identifying a pattern based on the provided formula.

Given \( h(n) = -13n \), we can calculate the first few values:

- \( h(1) = -13 \cdot 1 = -13 \)
- \( h(2) = -13 \cdot 2 = -26 \)
- \( h(3) = -13 \cdot 3 = -39 \)

Now, looking at the differences, we can see that the difference between successive terms is constant:

- \( h(2) - h(1) = -26 - (-13) = -13 \)
- \( h(3) - h(2) = -39 - (-26) = -13 \)

This shows that \( h(n) \) has a constant first difference of \(-13\), which means the recursive relationship can be established.

The recursive formula can be expressed as:
- \( h(1) = -13 \)
- \( h(n) = h(n-1) - 13 \) for \( n > 1 \)

Thus, the complete recursive definition is:

\[
h(1) = -13
\]
\[
h(n) = h(n-1) - 13 \quad \text{for } n > 1
\]