Here is the recursive definition of a sequence: \(f(1)=35, f(n) = f(n-1) - 8\) for \(n\ge2\).

1. List the first 5 terms of the sequence.

2. Graph the value of each term as a function of the term number.

Here is a graph of sequence \(q\). Use function notation to define \(q\) recursively.

Graph of a sequence Q. Horizontal axis, "n," with scale from 0 to 6, by 1’s. Vertical axis, with scale negative 5 to 10 by 1’s. Coordinates plotted (1 comma negative 3), (2 comma 0), (3 comma 3), (4 comma 6) and (5 comma 9).

Here is a recursive definition for a sequence \(f\): \(f(0) = 19, f(n) = f(n-1) - 6\) for \(n \geq 1\). The definition for the \(n^{\text{th}}\) term is \(f(n) = 19 - 6 \boldcdot n\) for \(n\ge0\).

1. Explain how you know that these definitions represent the same sequence.
2. Select a definition to calculate \(f(20)\), and explain why you chose it.

An arithmetic sequence \(j\) starts 20, 16, . . . Explain how you would calculate the value of the 500th term.