Bell Ringer 15.notebook
February 22, 2016
Bell Ringer 15
a. Find the first five terms in the sequence in which a1 = ­8 and an = ­2an­1 + 5, if n > 2.
b. Write a recursive formula for the following sequence:
4, 10, 25, 62.5 ...
c. Write a recursive formula for the following sequence:
9, 36, 63, 90 ...
Homework 7.8 due Tuesday:
Pg. 448 ­ 450 (10 ­ 58, every 4th)
Quiz on Wednesday!
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Bell Ringer 15.notebook
February 22, 2016
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Bell Ringer 15.notebook
February 22, 2016
Lesson Objectives:
­ Use a recursive formula to list terms in a sequence.
­ Write recursive formulas for arithmetic and geometric sequences.
Vocab terms:
Recursive Formula ­ formula that allows you to find the nth term of a sequence by performing operations to one or more of the preceding terms.
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Bell Ringer 15.notebook
February 22, 2016
Use a recursive formula:
a. Find the first five terms of the sequence in which a1 = 7 and an = 3an­1 ­ 12, if n > 2.
b. Find the first five terms of the sequence in which a1 = ­2 and an = (­3)an­1 + 4, if n > 2.
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Bell Ringer 15.notebook
February 22, 2016
Steps for writing a recursive formula:
Step 1:
Determine if the sequence is arithmetic or geometric.
Step 2:
Arithmetic sequence:
an = an­1 + d where d is the common difference
Geometric sequence:
an = (r)an­1 where r is the common ratio.
Step 3:
State the first term a1 and the domain for n.
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Bell Ringer 15.notebook
February 22, 2016
Writing recursive formulas:
a. 17, 13, 9, 5 ...
b. 6, 24, 96, 384 ...
c. 4, 10, 25, 62.5 ...
d. 9, 36, 63, 90 ...
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Bell Ringer 15.notebook
February 22, 2016
Recursive and Explicit Formulas:
Given the sequence write a recursive and explicit formula:
a. 12,000; 7,200; 4,320; 2,592 ...
b. 10,000; 10,300; 10,609; 10,927.27 ...
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Bell Ringer 15.notebook
February 22, 2016
Going from Recursive to Explicit and vice versa:
a. an = 6n + 3
b. a1 = 120, an = .8an­1, n > 2.
c. an = (4/3)(3)n
d. a1 = ­16, an = an­1 ­ 7, n > 2
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Bell Ringer 15.notebook
February 22, 2016
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