Recursive Formulas for Sequences Algebra II CP Mrs. Sweet

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Recursive Formulas for Sequences Algebra II CP Mrs. Sweet Outline Section 1-8 Recursive Formulas for Sequences Algebra II CP Mrs. Sweet

Use your calculator to generate the following sequence: 40, 20, 10, 5, 2.5,… What is the rule for generating the sequence? Divide the previous term by 2 Find the next 3 terms of the sequence: 1.25, .625, .3125, … What must you know before you can compute the 12th term of the sequence? What the 11th term was.

A Formula is a rule for finding a term of a sequence by applying the rule to the term before it. Recursive Recursive Formulas have parts:

Part II: Part I: Indicates the first term (or the first few terms) previous term divided by 2 for all terms after the first Part II: Tells how the nth term is related to one or more of the previous terms.

Examples: 1) Find the pattern and express it as a recursive formula The previous term plus 3

Examples: 1) Find the pattern and express it as a recursive formula b) 2, 7, 12, 17, 22, … 2 Five more than the previous term

2) Given the recursive formula use your calculator to find the first 5 terms of the sequence: Previous term +4 for integers n > 2 3 times the previous term -1 for integers n > 2

3) Louis is trying to learn a very long and difficult piano piece that had 400 measures. After learning the first page which has 24 measures, he decided that he would learn 4 measures a day. The sequence 28, 32, 36, 40 … gives the number of measures he will have learned after n days. a) In words, describe this sequence recursively: Louis will learn 24 measures from the first page and then will add 4 measures each day. b) Write a recursive formula for this sequence using the ANS key on your calculator: ANS Plus 4

Examples: 1) a) What is the fourth term? b) Find c) What sequence is generated by this explicit formula? d) Write a recursive formula for this sequence.

2) 1, 4, 9, 16, 25, 36, …. a) What is the value of ? b) Give an explicit formula for

c) Write an explicit formula for 3) Given the sequence 2, 4, 6, 8, 10,… a) What is the 3rd term? b) What is the value of ? c) Write an explicit formula for d) Use this formula to find e) Write a recursive formula for this sequence

4) In the sequence 1, 8, 27, 64, 125, 216,… a) What is the value of ? b) Write an explicit formula for d) Use this formula to find