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Use your calculator to generate the following sequence: 40, 20, 10, 5, 2.5,… What is the rule for generating the sequence? Divide the previous term by 2 Find the next 3 terms of the sequence: 1.25, .625, .3125, … What must you know before you can compute the 12th term of the sequence? What the 11th term was.
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Outline Section 1-8Outline Section 1-8Recursive Formulas for Recursive Formulas for SequencesSequencesAlgebra II CPAlgebra II CP
Mrs. SweetMrs. Sweet
Use your calculator to generate the following sequence: 40, 20, 10, 5, 2.5,…
What is the rule for generating the sequence?
Divide the previous term by 2
Find the next 3 terms of the sequence:
1.25, .625, .3125, …
What must you know before you can compute the 12th term of the sequence?
What the 11th term was.
A Formula is a rule for finding a term of a sequence by applying the rule to the term before it.
Recursive Formulas have parts:
Recursive
Part I:Indicates the first term (or the first few terms)
1 40t
Part II:Tells how the nth term is related to one or more of the previous terms.
previous term divided by 2 for all terms after the first
nt
Examples:1) Find the pattern and express it as a recursive formula
a) 1, 4, 7, 10, 13, 16, …
1t
nt
1The previous term plus 3
Examples:1) Find the pattern and express it as a recursive formula
b) 2, 7, 12, 17, 22, …
nt
1t
nt
2Five more than the previous term
2) Given the recursive formula use your calculator to find the first 5 terms of the sequence:
1 3
n
tt
Previous term
+4for integers n > 2
1 1
n
SS
3 times the previous
term -1
for integers n > 2
3) Louis is trying to learn a very long and difficult piano piece that had 400 measures. After learning the first page which has 24 measures, he decided that he would learn 4 measures a day. The sequence 28, 32, 36, 40 … gives the number of measures he will have learned after n days.
a) In words, describe this sequence recursively:Louis will learn 24 measures from the first page and then will add 4 measures each day.
b) Write a recursive formula for this sequence using the ANS key on your calculator:
1 28
n
tt
ANS Plus 4
Examples:1)
a) What is the fourth term?
b) Find
15 2 1nt n
8t
8t
c) What sequence is generated by this explicit formula?
d) Write a recursive formula for this sequence.
2) 1, 4, 9, 16, 25, 36, ….
a) What is the value of ?
b) Give an explicit formula for
4t
nt
3) Given the sequence 2, 4, 6, 8, 10,…
a) What is the 3rd term?
b) What is the value of ?
c) Write an explicit formula for
d) Use this formula to find
8t
nt
27t
e) Write a recursive formula for this sequence
4) In the sequence 1, 8, 27, 64, 125, 216,…
a) What is the value of ?
b) Write an explicit formula for
d) Use this formula to find
nt
10t
5t
