Transcript 3.5 Arithmetic Sequences as Linear Functions

3.5 Arithmetic Sequences as
Linear Functions
Objective:
1) Use inductive reasoning in
continuing number patterns
2) Write rules for arithmetic
sequences
3) Relate arithmetic sequences to
linear functions
Vocabulary
• Inductive reasoning: Making
conclusions based on patterns you
observe.
• Sequence: a set of numbers in a
specific order
• Terms: the numbers in a sequence
Vocabulary Continued
• Arithmetic Sequence: A numerical
pattern that increase or decrease at a
constant rate or value.
• Common Difference: The difference
between the terms in a sequence.
Represented by the letter d.
Find the next two numbers in each
pattern and describe the pattern
a) 2, 5, 8, 11,…
b) 2, 4, 6, 8,…
c) 1, 9, 17, 25, …
Determine whether the sequence is an
arithmetic sequence if so what is the
pattern?
-4, -2, 0, 2,…
Determine whether the sequence
is an arithmetic sequence if so
what is the pattern?
-26, -22, -18, -14,…
Determine whether the sequence
is an arithmetic sequence if so
what is the pattern?
1, 4, 9, 25, …
Determine whether the sequence
is an arithmetic sequence if so
what is the pattern?
1 5 3 13
, , , ,...
2 8 4 16
Find the nth term
an  a1  (n  1)d
a1= first term of sequence
d= common difference
**** n must be positive ****
Write an equation for the nth
term of the arithmetic sequence
-12, -8, -4, 0, …
Find the
th
9
term of the sequence
Which term of the sequence is
32?
You Try
Consider the arithmetic sequence
3, -10, -23, -36, …
a) Write an equation for the nth term of
the sequence
b) Find the 15th term in the sequence
c) Which term of the sequence is –114?
Arithmetic Sequences as
Functions
Marisol is mailing invitations for her
quinceanera. The arithmetic sequence
$0.41, $0.82, $1.23, $1.64, … represents the
cost of postage.
a) Write a function to
represent this sequence
Write an arithmetic
sequence on a blank piece
of paper.