2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016
Wednesday, 11/2/2016
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Text Section 4.6
pg. 214-216 # 23-49 odd
Homework Questions?
For the following arithmetic sequences, find the common difference and
formula for an.
1)
2)
3)
2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016
Given the explicit formula, find the first 2 terms and the specified term.
4)
5)
Given the first term in the sequence and the common difference, find
the 1st five terms of the sequence.
6)
7)
2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016
Does the graph show an Arithmetic Sequence? Explain.
(4, 2)
(6, 3)
(2, 1)
(8, 2)
(10, 1)
Anna is setting up chairs for a friends wedding. The front row
will have 5 chairs and each row behind it will have 3 more chairs
than the row before. How many chairs in the 11th row?
For the following arithmetic sequences, find the common difference and
formula for an .
1) ­15, ­11, ­7, ­3, ...
2) 1000, 898, 796, 694, ...
3) ­3, 15, 33, 51, ...
2016­11­2 Intro to Recursive Formulas .notebook
A carnival charges $2 for each game after you pay a $4 entry fee.
a. Write a function that represents the arithmetic sequence.
b. Graph the function.
c. How many games can you play when you take $28 to the carnival?
Games
1
Total Cost
$6 $8 $10 $12
2
3
4
Recursion is the process of choosing a starting term
and repeatedly applying the same process
to each term to arrive at the following term.
Finding the recursive formula, requires us to know the initial
value and the "rule", i.e., common difference.
Ex.
­15, ­11, ­7, ­3, ...
5, 8, 11, 14, 17
November 02, 2016
2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016
A recursive formula always has two parts:
1. The starting value for a1.
2. The recursion equation for an as a function
of the term before it.
a1 a2 a3 a4
Sequence: 5, 8, 11, 14, ...
Starting value: a1
Rule:
Recursion Equation:
Consider a sequence given by the formula
an = an-1 - 5 , where a1 = 12 and n > 1
List the first 5 numbers in the sequence:
2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016
Find the first 4 numbers in the sequence if:
f(1) = 3
f(n) = f(n-1) - 2
Consider the sequence 2, 4, 6, 8, 10, ...
Write a recursive formula:
a1 =
an =
2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016
Consider the sequence -3, -9, -15, -21, ...
Write a recursive formula:
a1 =
an =
Write a recursive formula for the sequence
9, 3, -3, -9, ...
f(1) =
f(n) =
2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016
Using the sequence:
-4, -6, -8, -10, ...
Write :
Explicit Formula: _______________
Recursive Formula:______________
If you wanted to find the 6th term of the sequence which
equation can you use?
If you wanted to find the 100th term of the sequence which
equation would you use?
What are the two types of formulas
to write a sequence?
SUMMARY
Explicit formula specifies the nth term
of a sequence as an expression in n.
Recursive formula specifies the nth term
of a sequence as an expression in the
previous term.
2016­11­2 Intro to Recursive Formulas .notebook
November 02, 2016