Warm up.

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Presentation transcript:

Warm up

Homework Questions

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.

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.

Example 1 identify arithmetic sequences Tell whether the sequence is arithmetic. a. – 4, 1, 6, 11, 16, . . . b. 3, 5, 9, 15, 23, . . .

Example 2 write the rule for the nth term Write a rule for the nth term of the sequence. Then find a15. a. 1. 4, 9, 14, 19, . . . 2. 60, 52, 44, 36, . . .

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, . . .

Example 3 write the rule given a term and common difference 1. 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.

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

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

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.

Homework Questions

Homework Questions

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.

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.

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

Example 5 standardized test practice

Sum of the arithmetic series

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.

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