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