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GUIDED NOTES – Lesson 8-5 Recursive Sequences Name: ______________________ Period: ___ STANDARD: (F-BF.2) Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.OBJECTIVES: I can…Find terms for a sequence using a recursive formula.Write a recursive formula to represent a given sequence.So far we have focused on sequences generated by an explicit formula, where the value of each term relates directly to the position of that termIn recursive formulas, each succeeding term is formulate from one or more previous terms. Recursive formulas have two parts:A) The value(s) of the first term(s)B) An equation that shows how to find each term based on the term(s) before it.EXAMPLES:A) Find the first five terms of the sequence in which a1 = 5 and an = an-1 + 3B) Find the first five terms of the sequence in which a1 = 2, a2 = 5 and an = 3an-1 – 1C) Find the first five terms of the sequence in which a1 = 3, a2 = 5 and an = 2an-2 + nD) Find the first five terms of the sequence in which a1 = 3, a2 = 4 and an = 2an-2 – an-1Writing Recursive FormulasDecide if it is arithmetic or geometricFind the common difference or ratioWrite the formulaEXAMPLES:E) Write a recursive formula for the sequence: 2, 10, 18, 26, 34, …F) Write a recursive formula for the sequence: 15, 17, 19, 21, 23, 25, …G) Write a recursive formula for the sequence: 20, 18, 17, 15, 14, 12, …H) Write a recursive formula for the sequence: 16, 56, 196, 686, 2401, …I) Write a recursive formula for the sequence: 6, 13, 27, 55, … ................
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