1. Arithmetic Sequences and Series

2. Arithmetic Sequences

3. An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

4. Which of the following sequences are arithmetic
Which of the following sequences are arithmetic? Identify the common difference.
YES
YES NO NO
YES

5. The common difference is always the difference between any term and the term that proceeds that term.
Common Difference = 5

6. The general form of an ARITHMETIC sequence.
First Term:
Second Term:
Third Term:
Fourth Term:
Fifth Term:
nth Term:

7. Formula for the nth term of an ARITHMETIC sequence.
If we know any three of these we ought to be able to find the fourth.

8. Given:
Find:
IDENTIFY
SOLVE

9. Find: What term number is -169?
Given:
Find: What term number is -169?
IDENTIFY
SOLVE

10. Given:
Find:
What’s the real question?
The Difference
IDENTIFY
SOLVE

11. Given:
Find:
IDENTIFY
SOLVE

12. Arithmetic Series

13. Write the first three terms and the last two terms of the following arithmetic series.
What is the sum of this series?

14. What is the SUM of these terms?
Written 1st to last.
Written last to 1st.
Add Down
50 Terms
71 + (-27) Each sum is the same.

15. In General . . .

16. Find the sum of the terms of this arithmetic series.

17. Find the sum of the terms of this arithmetic series.
What term is -5?

18. Alternate formula for the sum of an Arithmetic Series.

19. Find the sum of this series
It is not convenient to find the last term.

20. Your Turn