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What is a Recursion Formula? A recursion formula consists of at least 2 parts. One part gives the value(s) of the first term(s) in the sequence, and the other part gives an equation that can be used to calculate each of the other terms from the term(s) before it. n must be integers, normally natural numbers

Example 1 – Recursion Formula Given the recursion formula a) Write the first 4 terms of each sequence. b)Identify the type of sequence. c) Find t 20 d) Find t n The first 4 terms are {11, 7, 3,-1} Remark: To calculate any term we need to calculate all terms before it. This is a bit of a drawback b) Arithmetic Sequence a = 11 d = -4 c & d) Recall Explicit formula 20

Example 2 – Recursion Formula Given the recursion formula a) Write the first 4 terms of each sequence. b)Identify the type of sequence. c) Find t 15 d) Find t n The first 4 terms are {2, -6, 18,-54} b) Geometric Sequence a = 2 r = -3 c & d) Recall Explicit formula 15

Example 3 – Construct Recursion Formulas Construct a recursion formula to represent the following sequences: a) {5,7,9,11,13...} b) {-2, 6, -18, 54,...} = 5 +2 Therefore, by observations, the recursion formula is: a) {5,7,9,11,13...} = 7 +2 = 9 +2 = -2(-3) Therefore, by observations, the recursion formula is: b) {-2, 6, -18, 54,...} =6(-3) = -18(-3) Geometric Sequence Arithmetic Sequence Expect Common Difference (d) Expect Common Ratio (r)

Homework: Check the web site Handout: Applications of Sequences More Sequences Practice