# Lesson 7

Representing More Sequences

### Problem 1

Here is the recursive definition of a sequence: \(f(1) = 10, f(n) = f(n-1) - 1.5\) for \(n\ge2\).

- Is this sequence arithmetic, geometric, or neither?
- List at least the first five terms of the sequence.
- Graph the value of the term \(f(n)\) as a function of the term number \(n\) for at least the first five terms of the sequence.

### Solution

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### Problem 2

An arithmetic sequence \(k\) starts 12, 6, . . .

- Write a recursive definition for this sequence.
- Graph at least the first five terms of the sequence.

### Solution

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### Problem 3

An arithmetic sequence \(a\) begins 11, 7, . . .

- Write a recursive definition for this sequence using function notation.
- Sketch a graph of the first 5 terms of \(a\).
- Explain how to use the recursive definition to find \(a(100)\). (Don't actually determine the value.)

### Solution

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(From Unit 1, Lesson 6.)### Problem 4

A geometric sequence \(g\) starts 80, 40, . . .

- Write a recursive definition for this sequence using function notation.
- Use your definition to make a table of values for \(g(n)\) for the first 6 terms.
- Explain how to use the recursive definition to find \(g(100)\). (Don't actually determine the value.)

### Solution

### Problem 5

Match each recursive definition with one of the sequences.

### Solution

### Problem 6

For each sequence, decide whether it could be arithmetic, geometric, or neither.

- 25, 5, 1, . . .
- 25, 19, 13, . . .
- 4, 9, 16, . . .
- 50, 60, 70, . . .
- \(\frac{1}{2},\) 3, 18, . . .

For each sequence that is neither arithmetic nor geometric, how can you change a single number to make it an arithmetic sequence? A geometric sequence?