1. Arithmetic Sequences
Unit 6 Notes

2. Vocabulary

3. Vocabulary Finite sequence – has a limited number of terms.
Infinite sequence – continues without stopping.

4. What does arithmetic mean?
An arithmetic sequence is a list of numbers with a common difference
A common difference means you are ADDING OR SUBTRACTING the same amount between each term.

5. HW: 1-6 Example 1 Determine if the sequence is arithmetic.
If so, find the common difference.
1) 2, 5, 8, 11, … 2) -2, 0, 3, 7, …
3) 3, 1, -1, -3, …
HW: 1-6

6. Ex. 2 Using an Explicit Formula Given the explicit formula for an arithmetic sequence find the first five terms and the 35th term
Term #
Work
Term 1
(1)
-10 2
(2) -8 3
(3) -6 4
(4) -4 5
(5) -2 35
(35) 58
HW: 7-10

7. You Try!
Write the first five terms and the 21st term given the explicit formula
HW: 7-10

8. Explicit Formula for Arithmetic Sequences
YOU NEED TWO THINGS EVERY TIME:
d (common difference)
(first term)
Memorize This One Kids!!!
𝑎 1

9. Ex.3 Given the first term and the common difference of an arithmetic sequence find the 1st 5 terms and the explicit formula
HW: 11-14

10. You Try!
HW: 11-14

11. Given a term in an arithmetic sequence and the common difference find the explicit formula
Solve for first term
and then write
explicit formula
𝟐𝟓 = 𝒂 𝟏 +(𝟏𝟏−𝟏)(−𝟑)
𝟐𝟓= 𝒂 𝟏 −𝟑𝟎
𝟓𝟓= 𝒂 𝟏
HW: 15-18

12. Ex.4 Given a term in an arithmetic sequence and the common difference find the explicit formula
HW: 15-18

13. Homework
Handout #1-18