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Sec. 3.4
Arithmetic Sequences
A sequence is a set of numbers, called terms, in a specific order.
If the difference between successive terms is constant, then it is called an arithmetic sequence.
The difference between the terms is called the common difference.
Ex. 1 Identify Arithmetic Sequences
Determine whether each sequence is arithmetic. Explain.
a.
1, 2, 4, 8, …
b.
1/2, 1/4, 0, -1/4, …
Your Turn
-26, -22, -18, -14, …
You can use the common difference of an arithmetic sequence to find the next terms in the sequence.
Ex. 2 Real-World Example
The arithmetic sequence 74, 67, 60, 53, … represents the amount of money that Tiffany owes her mother
at the end of each week. Find the next three terms.
Your Turn
Find the next four terms 9.5, 11.0, 12.5, 14.0, …
nth Term of an Arithmetic Sequence
The nth term an of an arithmetic sequence with first term a1, and common difference d is given by
Ex. 3 Real-World Example
The arithmetic sequence 12, 23, 34, 45, … represents the total number of ounces that a box weights after
each additional book is added.
a.
Write an equation for the nth term of the sequence.
b.
Find the 10th term in the sequence.
c.
Graph the first five terms of the sequence.
Your Turn
Consider the arithmetic sequence 3, -10, -23, -36, …
a.
Write an equation for the nth terms of the sequence.
b.
Find the 15th term in the sequence.