1. Warm Up State the pattern for each step.
3, 6, 9, 12, 15, 18, 21, 24, …
25, 20, 15, 10, 5, 0, -5, -10, …
-21, 3, 27, 51, 75, 99, 123, …

2. Arithmetic Sequences

3. Arithmetic Sequence
An arithmetic sequence is defined as a sequence in which there is a common difference between consecutive terms.
Common Difference = 5

4. Is the given sequence arithmetic? If so, identify the common difference.
2, 4, 8, 16, …
4, 6, 12, 18, 24, …
2, 5, 7, 12, …
48, 45, 42, 39, …
1, 4, 9, 16, …
10, 20, 30, 40, …

5. Arithmetic Sequence Formula
The 1st number in the sequence.
The common difference.
an = a1 + (n – 1) • d
The same as the n in an. If you’re looking for the 5th number in the sequence, n = 5.
The “nth” number in the sequence. Ex. a5 is the 5th number in the sequence.

6. Example 1:
an = a1 + (n – 1) • d
Given the sequence -4, 5, 14, 23, 32, 41, 50,…, find the 14th term.

7. Example 2:
an = a1 + (n – 1) • d
Given the sequence 6, 10, 14, 18, 22, 26,…, find the 17th term.

8. Example 3:
an = a1 + (n – 1) • d
Given the sequence 81, 80.5, 80, 79.5, 70,…, find the 9th term.

9. Example 4:
an = a1 + (n – 1) • d
Given the sequence 79, 75, 71, 67, 63,…, find the term number that is -169.

10. Example 5:
an = a1 + (n – 1) • d
Suppose you are saving up for a new gaming system. You have 100 dollars this year, and you plan to add 33 dollars each of the following years. How much money will you have in 7 years?

11. Arithmetic Mean
Used to find the missing term of an arithmetic sequence
Add the numbers and divide by two.

12. Find the missing term of the arithmetic sequence