1. Warmup
Solve the following systems of equations by the method of your choice:
1) )

2. What are partial sums of arithmetic sequences related to?
Acc. Alg/Geom A
UNIT QUESTION: How is a geometric sequence like an exponential function?
Standard: MM2A2, MM2A3
Today’s Question:
What are partial sums of arithmetic sequences related to?
Standard: MM2A3d

3. Arithmetic Sequences & Series

4. Arithmetic Sequence

5. Arithmetic Sequence
An arithmetic sequence is a list of numbers that are all separated by a common difference.
The sequence, and any specific term in it, can be generated using the formula

6. the nth term
the first term
the common difference
the number of the term you seek (i.e., if you want the 4th term, use a 4)

7. Let’s try it out:
7, 11, 15, 19, 23, …… What is the formula for this sequence? What is the 213th term?

8. Let’s try it out:
25, 17, 9, 1, -7, …… What is the formula for this sequence? What is the 137th term?

9. Let’s try it out:
-12, -7, -2, 3, 8, …… What is the formula for this sequence? What is the 384th term?

10. Let’s try it out:
What is the formula for this sequence? What is the 36th term?

11. Arithmetic Series

12. Arithmetic Series Series: sum of the terms of part of a sequence
Can be written in sigma notation form
Two methods:
Finding all terms & adding them
Formula

13. Finding all terms and adding
Find the sum of the first 7 terms

14. Find the sum of the first 7 terms
Using a formula
Find the sum of the first 7 terms

15. Sigma Notation
Discuss what each part of the notation means…

16. Find the sum of the first 50 terms
Have students find the sum using formula. Discuss why it’s so small (sequence is decreasing).
How would this be written in sigma notation? What is the total?

17. Solve

18. Solve
Cannot use the formula

19. Mixed Practice worksheet
Homework
Mixed Practice worksheet