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Unit 7 Section 1: Sequence: Explicit and Recursive Formulas

(Sequences can be either infinite or finite) A sequence is an ordered set of numbers where each number is called a term of the sequence. -2, 5, 12, 19, 26, … (Sequences can be either infinite or finite) 1st Term 𝒂 𝟏 2nd Term 𝒂 𝟐 3rd Term 𝒂 𝟑 4th Term 𝒂 𝟒 5th Term 𝒂 𝟓

Recursive Formula Recursively defined sequences are given so that finding each new term depends on knowing the prior term. 𝒂 𝟏 =𝟑, 𝒂 𝒏 =𝟏𝟐+ 𝒂 𝒏−𝟏 3, 15, 27, 39, … 𝒂 𝟏 =𝟑 𝒂 𝟐 = 𝒂 𝟏 +𝟏𝟐 𝒂 𝟑 = 𝒂 𝟐 +𝟏𝟐 𝒂 𝟒 = 𝒂 𝟑 +𝟏𝟐

Try it… find the first 5 terms 1) 𝒂 𝟏 =𝟐 and 𝒂 𝒏 = 𝒂 𝒏−𝟏 𝟐 𝟐

Explicit Formula 𝒂 𝒏 =𝟏𝟐𝒏−𝟗 3, 15, 27, 39, … Explicitly defined sequences are given so that finding each term depends on what number the term is in the sequence. 𝒂 𝒏 =𝟏𝟐𝒏−𝟗 3, 15, 27, 39, … 𝒂 𝟏 =𝟏𝟐 𝟏 −𝟗 𝒂 𝟐 =𝟏𝟐 𝟐 −𝟗 𝒂 𝟑 =𝟏𝟐 𝟑 −𝟗 𝒂 𝟒 =𝟏𝟐 𝟒 −𝟗

Try it… find the first 5 terms or write a explicit formula 1) 𝒂 𝒏 =𝒏(𝒏+𝟑) 2) 1, 3, 7, 15, 31,…