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Arithmetic Recursive and Explicit formulas

Arithmetic Recursive and Explicit formulas. I can write explicit and recursive formulas given a sequence. Day 2. An ordered list of numbers defined by a starting value (number) and a rule to find the general term. Recursive Formula:. review. A(1) =. first term. A(n-1)=. Previous term.

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Arithmetic Recursive and Explicit formulas

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  1. Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2

  2. An ordered list of numbers defined by a starting value (number) and a rule to find the general term. Recursive Formula: review A(1)= first term A(n-1)= Previous term A(n)= General term or nth term Given the following recursive formula, find the first 4 terms. 20, 26, 32, 38 A(1)= 20 A(n)= A(n-1) + 6 1st term2nd term3rd term 4th term A(1)= 20 A(n-1) + 6 A(n)= A(n-1) + 6 A(n)= A(2)= A(2-1) + 6 A(3)= A(3-1) + 6 A(2)= A(1) + 6 A(3)= A(2) + 6 A(2)= 20 + 6 A(3)= 26 + 6 A(2)= 26 A(3)= 32

  3. Explicit Formula: a function rule that relates each term of the sequence to the term number. A(n) = A(1) + (n-1)d Common difference 1st term nth term Term number Write an explicit formula given the following sequence and then find the 5th term. 20, 26, 32, … 44 Find it without the formula: 20, 26, 32, ___, ____, 38 Now, write and use the formula to find the 5th term: A(n) = A(1) + (n -1)d 5 20 6 n = A( ) = + ( -1) 5 5 20 A(1) = A( 5) = 20 + (4)6 6 d = A( 5) = 44

  4. Write an explicit formula for each recursive formula. A(1) = 19 A(n) = A(n-1) + 12 A(1) = 5 A(n) = A(n-1) - 3 A(n) = A(1) + (n-1)d A(n) = A(1) + (n-1)d A(n) = + (n-1) 19 A(n) = + (n-1) 5 (-3) 12 Find the 2nd, and 10th terms of the sequence on the left.. 10 19 19 2 12 10 A() = + ( - 1) 12 A() = + ( -1) 2 A( 10) = 19 + (9) 12 A(2) = 19 + (1)12 A( 10) = 19 + 108 A(2) = 19 + 12 A( 10) = 127 A(2) = 31

  5. Write a recursive formula for each explicit formula. A(n) = 32 + (n -1)12 A(n) = 32 + (n -1)12 A(1) = A(n) = A(n-1) 32 + 12 A(n) = 10 + (n -1)(- 4) A(n) = 10 + (n -1)(- 4) A(1) = A(n) = A(n-1) 10 Assignment: Page 279: 38-44 evens, 46-53, 66-67, 76,77, 80 - 4

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