Arithmetic Recursive and Explicit formulas I can write
- Slides: 5
Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2
Recursive Formula: An ordered list of numbers defined by a starting value (number) and a rule to find the general term. 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 1 st term 2 nd term 3 rd term 4 th term A(n) = A(n-1) + 6 A(1) = 20 A(n) = A(n-1) + 6 A(2) = A(3) = A(3 -1) + 6 A(2 -1) + 6 A(1) + 6 20 + 6 26 A(3) = A(2) + 6 A(3) = 26 + 6 A(3) = 32
Explicit Formula: a function rule that relates each term of the sequence to the term number. A(n) = A(1) + (n-1)d nth term 1 st term Term number Common difference Write an explicit formula given the following sequence and then find the 5 th term. 20, 26, 32, … Find it without the formula: 44 20, 26, 32, ___, 38 ____, Now, write and use the formula to find the 5 th term: A(n) = A(1) + (n -1)d A( 5) = 20 + ( 5 -1) 6 A( 5) = 20 + (4)6 A( 5) = 44 n= 5 A(1) = 20 d= 6
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) = 19 + (n-1) 12 A(n) = 5 + (n-1) (-3) Find the 2 nd, and 10 th terms of the sequence on the left. . A(2) = 19 + (1)12 A( 10 ) =19 + (10 - 1)12 A( 10) = 19 + (9) 12 A(2) = 19 + 12 A( 10) = 19 + 108 A(2) = 31 A( 10) = 127 A( 2 ) = 19 + ( 2 -1) 12
Write a recursive formula for each explicit formula. A(n) = 32 + (n -1)12 A(1) = 32 A(n) = A(n-1) + 12 A(n) = 10 + (n -1)(- 4) A(1) = 10 A(n) = A(n-1) - 4 Assignment: Page 279: 38 -44 evens, 46 -53, 66 -67, 76, 77, 80
