# 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 $$n\ge2$$.

1. Is this sequence arithmetic, geometric, or neither?
2. List at least the first five terms of the sequence.
3. 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.

### Problem 2

An arithmetic sequence $$k$$ starts 12, 6, . . .

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

### Problem 3

An arithmetic sequence $$a$$ begins 11, 7, . . .

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

### Solution

(From Unit 1, Lesson 6.)

### Problem 4

A geometric sequence $$g$$ starts 80, 40, . . .

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

### Solution

(From Unit 1, Lesson 6.)

### Problem 5

Match each recursive definition with one of the sequences.

### Solution

(From Unit 1, Lesson 5.)

### Problem 6

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

1. 25, 5, 1, . . .
2. 25, 19, 13, . . .
3. 4, 9, 16, . . .
4. 50, 60, 70, . . .
5. $$\frac{1}{2},$$ 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?