Transcript 3-4: Arithmetic Sequences

3-4: Arithmetic Sequences
 Sequence: a set of numbers in a specific order
 Terms: the numbers in a sequence
 Arithmetic Sequence: numerical pattern that
increases or decreases at a constant rate or value
 Common Difference: the constant difference
between the terms
Identify Arithmetic Sequences
 Determine whether each sequence is arithmetic.
Explain.

1, 2, 4, 8, …


No, because the difference between terms is not constant.
½, ¼, 0, -1/4, …

Yes, because the difference between terms is constant
 Check Your Progress #1A & 1B
Writing Arithmetic Sequences
 Each term of an arithmetic sequence after the first
term can be found by adding the common difference
to the preceding term.
 An arithmetic sequence, a1, a2, …, can be found as
follows:


a1, a2 = a1 + d, a3 = a2 + d, a4 = a3 + d, …
Where d is the common difference, a1 is the first term, a2 is the
second term, and so on.
Writing Arithmetic Sequences
 The arithmetic sequence 66, 60, 54, 48, … represents
the amount of money that John needs to save at the
end of each week in order to buy a new game. Find
the next three terms.




Find the common difference by subtracting the successive
terms.
The common difference is -6
Add -6 to the last term of the sequence to get the next term.
Continue adding -6 until the next three terms are found.
48 – 6 = 42, 42 – 6 = 36, 36 – 6 = 30
 Check Your Progress #2
 Each term in an arithmetic sequence can be
expressed in terms of the first term a1 and the
common difference d.
Term
Symbol
In Terms of a1 and
d
Numbers
First
a1
a1
8
Second
a2
a1 + d
8 + 3 = 11
Third
a3
a1 + 2d
8 + 2(3) = 14
Fourth
a4
a1 + 3d
8 + 3(3) = 17
nth term
an
a1 + (n-1)d
8 + (n-1)(3)
 This leads to the formula that can be used to find
any term in an arithmetic sequence:

a1 + (n-1)d, where an is the nth term, a1 is the first term, and
d is the common difference. N must be a positive integer.
Example 3
 Page 167
 Check Your Progress #3A, 3B, & 3C
Homework
 Assignment #24
 Page 168 #12-38 even, 40-45, 50-52