# Lesson 10

Situations and Sequence Types

• Let’s decide what type of sequence we are looking at and how to represent it.

### Problem 1

A sequence is defined by $$f(0) = 3, f(n) = 2 \boldcdot f(n-1)$$ for $$n\ge1$$. Write a definition for the $$n^{\text{th}}$$ term of $$f$$.

### Problem 2

A geometric sequence, $$g(n)$$ starts 20, 60, . . . Define $$g$$ recursively and for the $$n^{\text{th}}$$ term.

### Problem 3

A geometric sequence $$g$$ starts at 500 and has a growth factor of 0.6. Sketch a graph of $$g$$ showing the first 5 terms.

(From Unit 1, Lesson 7.)

### Problem 4

1. An arithmetic sequence has $$a(1)=4$$ and $$a(2)=16$$. Explain or show how to find the value of $$a(15)$$
2. A geometric sequence has $$g(0)=4$$ and $$g(1)=16$$. Explain or show how to find the value of $$g(15)$$.
(From Unit 1, Lesson 8.)

### Problem 5

A piece of paper has an area of 96 square inches.

1. Complete the table with the area of the piece of paper $$A(n)$$, in square inches, after it is folded in half $$n$$ times.
2. Define $$A$$ for the $$n^{\text{th}}$$ term.
3. What is a reasonable domain for the function $$A$$? Explain how you know.
$$n$$ $$A(n)$$
0 96
1
2
3
(From Unit 1, Lesson 9.)

### Problem 6

Here is a growing pattern:

1. Describe how the number of dots increases from Stage 1 to Stage 3.
2. Write a definition for sequence $$D$$, so that $$D(n)$$ is the number of dots in Stage $$n$$.
3. Is $$D$$ a geometric sequence, an arithmetic sequence, or neither? Explain how you know.
(From Unit 1, Lesson 9.)

### Problem 7

A paper clip weighs 0.5 grams and an empty envelope weighs 6.75 grams.

1. Han adds paper clips one at a time to an empty envelope. Complete the table with the weight of the envelope $$w(n)$$, in grams, after $$n$$ paper clips have been added.
2. Does $$w(10.25)$$ make sense? Explain how you know.
$$n$$ $$w(n)$$
0 $$6.75$$
1
2
3
(From Unit 1, Lesson 9.)