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Chapter 11
Sequences and Series
11.1
Arithmetic Sequences
Key Terms

Sequence: an ordered list of numbers


1, 3, 5, 7, 9, ….
Terms: the numbers in the sequence

The 1st term in the sequence above is 1, 2nd is 3, 3rd is 5, etc

Arithmetic Sequence: a sequence in which each terms
after the 1st is found by adding a constant

Common difference: the number added to each term
in an arithmetic sequence
Arithmetic sequence Formula:
an = a1 + (n – 1)d
 an
= specific term (nth term)
 a1 = 1st term in the sequence
 n = number of position for given term
 d = common difference
Find the next four terms in the
sequence.
 -6,
-2, 2,….
 1.6,
1.1, 0.6, ….
Write
an equation for the nth term
10, 7, 4, 1, …
Write
an equation for the nth term
8, 17, 26, 35, …


The table shows typical costs for a construction
company to rent a crane for one, two, three, and
four months. If the sequence continues, how much
would it cost to rent the crane for a year?
Months
Cost ($)
1
75,000
2
90,000
3
105,000
4
120,000
The construction company has a budget of $350,000
for crane rental. The job is expected to last 18
months. Will the company be able to afford the
crane rental for the entire job? Explain.
Find the first 5 terms
for the sequence
described
 a1
= 2 d = 13
Find the indicated
term for the
sequence
 a1 =
20, d = 4, n = 81
Arithmetic Means
 The
terms between any two nonsuccessive terms in an arithmetic
sequence


Use the formula to find the common
difference
Then use the common difference to
calculate the arithmetic means
Find the arithmetic means
between the given terms
 16,__,
__, __, __, 91, …
 15.6,
__, __, __, 60.4, ...