1. Warm up

2. Homework Questions

3. 12.2 Arithmetic sequence
EQ: How can you tell a sequence is arithmetic?
Assessment: Students will write a summary about what makes a sequence arithmetic.

4. Arithmetic Sequence – the difference of consecutive terms is constant.
Key Terms
Arithmetic Sequence – the difference of consecutive terms is constant.
Common Difference – is the constant difference. Denoted by ‘d’
Arithmetic Series – the expression formed by adding the terms if an arithmetic sequence.

6. Example 1 identify arithmetic sequences
Tell whether the sequence is arithmetic.
a. – 4, 1, 6, 11, 16,
b , 5, 9, 15, 23, . . .

7. Example 2 write the rule for the nth term
Write a rule for the nth term of the sequence. Then find a15. a.
, 9, 14, 19, . . .
2. 60, 52, 44, 36, . . .

8. Example 2 write the rule for the nth term
b. Write a rule for the nth term of the arithmetic sequence. Then find a20.
17, 14, 11, 8, . . .

9. Example 3 write the rule given a term and common difference1.
One term of an arithmetic sequence is a19 = 48. The common difference is d = 3.
a. Write a rule for the nth term.
b. Graph the sequence.

10. Example 3 write the rule given a term and common difference2.
a11 = , d = − 1 2 .
a. Write a rule for the nth term.
b. Graph the sequence.

11. Homework Textbook Pg. 806 3-27 (3) and 29

12. Warm up 1.
Is the sequence 2, 103, 204, 305, 406, arithmetic? Explain your answer.
Write a rule for the nth term of the sequence 5, 2, –1, –4, Then find a5. 2.

13. Homework Questions

14. Homework Questions

15. Steps to Writing a Rule given two terms
Write a system of equations using an = a1 + (n – 1)d
and substitute for n.
STEP 2
Solve the system.
STEP 3
Find a rule for an.

16. Example 4 write a rule given two terms
a. Two terms of an arithmetic sequence are a8 = 21 and a27 = 97. Find a rule for the nth term.

17. Example 4 write a rule given two terms
b. Given a7 = 26, a16 = 71. Find a rule for the nth term.

19. Example 5 standardized test practice

20. Sum of the arithmetic series

21. Example 6 application House Of Cards
You are making a house of cards similar to the one shown
Write a rule for the number of cards in the nth row if the top row is row 1. a.
What is the total number of cards if the house of cards has 14 rows? b.

22. Homework Textbook Pg. 807- 808 31- 47(odd) and 63