Question

finally, what is the general term definition for this sequence?
13, 9, 5, 1, ...
recursive definition:
\

$$\begin{cases} f(0) = 13 \\\\ f(n) = f(n - 1) - 4 \\end{cases}$$

general term definition:
f(n) = ?n + \square

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence with first term \( f(0) = 13 \) and common difference \( d=-4 \).

Step2: Recall the arithmetic sequence formula

The general formula for an arithmetic sequence is \( f(n)=f(0)+dn \).

Step3: Substitute the values

Substitute \( f(0) = 13 \) and \( d=-4 \) into the formula: \( f(n)=13+(-4)n=-4n + 13 \).

Answer:

\( f(n)=-4n + 13 \) (So the coefficient of \( n \) is \(-4\) and the constant term is \(13\))