Lesson 8

A sequence is defined by \(f(0) = \text-20, f(n) = f(n-1) -5\) for \(n \ge1\).

1. Explain why \(f(1) = \text- 20 - 5\).
2. Explain why \(f(3) = \text- 20 - 5 - 5 - 5\).
3. Complete the expression: \(f(10)=\text-20-\underline{\hspace{.5in}}\). Explain your reasoning.

A sequence is defined by \(f(0) = \text- 4, f(n) = f(n-1) - 2\) for \(n\ge1\). Write a definition for the \(n^{\text{th}}\) term of the sequence.

Here is the recursive definition of a sequence: \(f(1) = 3,f(n) = 2 \boldcdot f(n-1)\) for \(n\ge2\).

1. Find the first 5 terms of the sequence.
2. Graph the value of the term as a function of the term number.
3. Is the sequence arithmetic, geometric, or neither? Explain how you know.

Write the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.

1. \(a(1) = 5, a(n) = a(n-1) + 3\) for \(n\ge2\).
2. \(b(1) = 1, b(n) = 3 \boldcdot b(n-1)\) for \(n\ge2\).
3. \(c(1) = 3, c(n) = \text-c(n-1) + 1\) for \(n\ge2\).
4. \(d(1) = 5, d(n) = d(n-1) + n\) for \(n\ge2\).