Lesson 78 Recursive Formulas with answers.notebook Questions/Main Ideas February 09, 2015 Lesson 78 Recursive Formulas recursive formula allows you to find the nth term of a sequence by performing operations to one or more of the preceding terms Example 1 Find the first 5 terms of the sequence in which a1 = 8, and an = 2an1 + 5 if n ≥ 2. Questions/Main Ideas Writing Recursive Formulas Step 1 Determine if the sequence is arithmetic or geometric by finding a common difference or a common ratio Step 2 Write a recursive formula Arithmetic Sequences: an = an1 + d where d is the common difference Geometric Sequences: an = r an1, where r is the common ratio Step 3 State the first term and domain for n. 1 Lesson 78 Recursive Formulas with answers.notebook Questions/Main Ideas February 09, 2015 Example 2 Write a recursive formula for each sequence. a. 23, 29, 35, 41, . . . b. 7, 21, 63, 189, . . . Questions/Main Ideas Explicit Formulas (learned in previous lessons) Arithmetic Sequence an = a1 + (n1)d Geometric Sequence an = a1 rn1 2 Lesson 78 Recursive Formulas with answers.notebook Questions/Main Ideas February 09, 2015 Example 3 The price of a car depreciates at the end of each year. a. Write a recursive formula for the sequence. b. Write an explicit formula for the sequence. Questions/Main Ideas Example 4 a. Write a recursive formula for an = 2n 4 b. Write an explicit formula for a1 = 84, an = 1.5an1, n ≥ 2 3 Lesson 78 Recursive Formulas with answers.notebook February 09, 2015 4 Lesson 78 Recursive Formulas with answers.notebook February 09, 2015 5 Lesson 78 Recursive Formulas with answers.notebook February 09, 2015 6
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