# Lesson 3

Different Types of Sequences

### Problem 1

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

1. -2, 4
2. 11, 111
3. 5, 7.5
4. 5, -4

What are the next three terms of each sequence?

### Solution

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### Problem 2

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

1. 200, 40, 8, . . .
2. 2, 4, 16, . . .
3. 10, 20, 30, . . .
4. 100, 20, 4, . . .
5. 6, 12, 18, . . .

### Solution

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### Problem 3

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

1. -3, -2, ___, ___, 1
2. ___, 13, 25, ___, ___
3. 1, .25, ___, -1.25, ___
4. 92, ___, ___ ,___, 80

### Solution

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### Problem 4

A sequence starts with the terms 1 and 10.

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

### Solution

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### Problem 5

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

1. ___, 5, 25, ___, 625
2. -1, ___, -36, 216, ___
3. 10, 5, ___, ___, 0.625
4. ___, ___, 36, -108, ___
5. ___, 12, 18, 27, ___

### Solution

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(From Unit 1, Lesson 2.)

### Problem 6

The first term of a sequence is 4.

1. Choose a growth factor and list the next 3 terms of a geometric sequence.
2. Choose a different growth factor and list the next 3 terms of a geometric sequence.

### Solution

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(From Unit 1, Lesson 2.)

### 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.

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

### Solution

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(From Unit 1, Lesson 1.)