# Lesson 3

Different Types of Sequences

- Let’s look at other types of sequences.

### Problem 1

Here are the first two terms of some different arithmetic sequences:

- -2, 4
- 11, 111
- 5, 7.5
- 5, -4

What are the next three terms of each sequence?

### Problem 2

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

- 200, 40, 8, . . .
- 2, 4, 16, . . .
- 10, 20, 30, . . .
- 100, 20, 4, . . .
- 6, 12, 18, . . .

### Problem 3

Complete each arithmetic sequence with its missing terms, then state the rate of change for each sequence.

- -3, -2, ___, ___, 1
- ___, 13, 25, ___, ___
- 1, .25, ___, -1.25, ___
- 92, ___, ___ ,___, 80

### Problem 4

A sequence starts with the terms 1 and 10.

- Find the next two terms if it is arithmetic: 1, 10, ___, ___.
- Find the next two terms if it is geometric: 1, 10, ___, ___.
- Find two possible next terms if it is neither arithmetic nor geometric: 1, 10, ___, ___.

### Problem 5

Complete each geometric sequence with the missing terms. Then find the growth factor for each.

- ___, 5, 25, ___, 625
- -1, ___, -36, 216, ___
- 10, 5, ___, ___, 0.625
- ___, ___, 36, -108, ___
- ___, 12, 18, 27, ___

### Problem 6

The first term of a sequence is 4.

- Choose a growth factor and list the next 3 terms of a geometric sequence.
- Choose a
*different*growth factor and list the next 3 terms of a geometric sequence.

### Problem 7

Here is a rule that can be used to build a sequence of numbers once a starting number is chosen: Each number is two times three less than the previous number.

- Starting with the number 0, build a sequence of 5 numbers.
- Starting with the number 3, build a sequence of 5 numbers.
- Can you choose a starting point so that the first 5 numbers in your sequence are all positive? Explain your reasoning.