Sequences as Linear Functions HS Algebra Objectives: Recognize arithmetic sequences; Relate arithmetic sequences to linear functions. What are sequences? A sequence is a set of numbers in a specific order. Sequences look for patterns between sets of numbers. Let’s look at this table. Find the rate of change for the time as the distance increases. The difference between the terms is called the _______________________________, which is denoted by d. Since the difference between successive terms is constant, this means the difference between the terms are all the same, we call this type of sequence an arithmetic sequence. Determine whether each sequence is an arithmetic sequence. Explain.
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Sequences as Linear Functions
HS Algebra
Objectives: Recognize arithmetic sequences; Relate arithmetic sequences to linear functions.
What are sequences?
A sequence is a set of numbers in a specific order. Sequences look for patterns between sets of numbers.
Let’s look at this table. Find the rate of change for the time as the distance increases.
The difference between the terms is called the _______________________________, which is denoted by d.
Since the difference between successive terms is constant, this means the difference between the terms are all the same, we call this type of sequence an arithmetic sequence.
Determine whether each sequence is an arithmetic sequence. Explain.
a) -4, -2, 0, 2, ... b) 12, 58, 34, 1316…
b) -26, -22, -18, -14,... d) 1, 4, 9. 25,…
Find the next three terms of the arithmetic sequence:
1. 15, 9, 3, -3…
2. 9.5, 11, 12.5, 14,…
Each term in an arithmetic sequence can be expressed in terms of the first term a1 and the common difference d.
The nth term of an arithmetic sequence with first term a1 and common difference d is given by:
where n is a positive integer.
a) Write an equation for the nth term of the arithmetic sequence -12, -8, -4, 0, …
b) Find the 9th term of the sequence.
c) Graph the first five terms of the sequence.
n an (n, an)1 -122 -83 -44 05
d) Which term of the sequence is 32?
Consider the arithmetic sequence 3, -10, -23, -36,…
a) Write an equation for the nth term of the sequence.
b) Find the 15th term of the sequence.
c) Graph the first five terms of the sequence
n an (n, an)1 32 -103 -234 -365
d) Which term of the sequence is -114?
Look at the graphs of the two arithmetic sequences we just graphed. What do you notice about the graphs? What types of graphs do arithmetic sequences create?
What is the independent variable? The dependent variable? The slope?
Melissa is mailing invitations for her bat mitzvah. The arithmetic sequence $0.42, $0.84, $1.26, $1.68,… represents the cost of postage.
a) Write a function to represent this sequence.
b) Graph the function
The chart below shows the length of Martin’s long jumps.
a) Write a function to represent this arithmetic sequence.
b) Graph the function
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