Title: Lesson 1-7
Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 1-9

EXAMPLE     Describe and Extend a Sequence
1. Describe the relationship between the terms in the arithmetic sequence 
 3, 9, 15, 21, …  Then write the next three terms in the sequence.

+6

+6

+6

3, 9, 15, 21, …

Each term is found by adding 6 to the previous term.  Continue the pattern to find the next three terms.
	21 + 6 = 27		27 + 6 = 33		33 + 6 = 39
The next three terms are 27, 33, and 39. 

EXAMPLE     Describe and Extend a Sequence
2. Describe the relationship between the terms in the sequence 1.3, 2.1, 2.9, 3.7, …  Then write the next three terms in the sequence.

+.8

+.8

+.8

1.3, 2.1, 2.9, 3.7, …

Each term is found by adding 0.8 to the previous term.  Continue the pattern to find the next three terms.
	3.7 + 0.8 = 4.5		4.5 + 0.8 = 5.3		5.3 + 0.8 = 6.1
The next three terms are 4.5, 5.3, and 6.1.

Real-World EXAMPLE
3. EXERCISE  Emily writes out an exercise plan for her summer vacation.  She plans to swim three laps each day during the first week of vacation and increase the number of laps by three each week after that.  If this pattern continues, what algebraic expression can be used to help her find the total number of laps she will swim daily during the tenth, and last, week of her summer vacation?  Use the expression to find the total.

Make a table to display the sequence.

Position | Operation | Value of Term
1 | 1 ⋅ 3 | 3
2 | 2 ⋅ 3 | 6
3 | 3 ⋅ 3 | 9
n | n ⋅ 3 | 3n

Each term is 3 times its position number.  So, the expression is 3n.

3n		Write the expression.
3(10) = 30		Replace n with 10.

So, during the final week of summer vacation, Emily will swim 30 laps each day.