Download Arithmetic Recursive and Explicit worksheet

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.
A(1) =first term
review
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
1st term 2nd term 3rd term 4th term
A(n) = A(n-1) + 6
A(1) = 20
A(n) = A(n-1) + 6
A(n) = A(n-1) + 6
A(2) = A(2-1) + 6
A(2) = A(1) + 6
A(3) = A(3-1) + 6
A(2) = 20 + 6
A(2) = 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
1st term
Term
number
Common
difference
Write an explicit formula given the following sequence and then find the 5th term.
20, 26, 32, …
Find it without the formula:
44
20, 26, 32, ___,
38 ____,
Now, write and use the formula to find the 5th 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) = A(1) + (n-1)d
A(n) = 19 + (n-1) 12
A(n) = 5 + (n-1) (-3)
Find the 2nd, and 10th 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