1. Warm up! Find the pattern for each set.
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. An arithmetic sequence is a sequence of numbers with a common difference.

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. Let’s name the terms!
2, 5, 8, 11, 14, 17, 20

6. Great! Now find a37!
2, 5, 8, 11, 14, 17, 20
Amazing! Now find a2943!

7. Arithmetic Sequence Formula
common difference
1st term
an = a1 + (n – 1) • d
nth term. For example, the 16th term would be a16
If you are solving for a16, just write 16 here

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

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

10. Example 3:
an = a1 + (n – 1) • d
Given the sequence 81, 80.5, 80, 79.5, 79,…, find the value of the 9th term.

11. Example 4:
an = a1 + (n – 1) • d
Given the sequence 79, 75, 71, 67, 63,…, find the term that has a value of -169.

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

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

14. Find the missing term of the arithmetic sequence