### Example 7-1a

```Determine whether –15, –13, –11, –9, ... is arithmetic.
–15
–13
+2
–11
+2
–9
+2
Answer: This is an arithmetic sequence because
the difference between terms is constant.
Determine whether
is arithmetic.
Answer: This is not an arithmetic sequence
because the difference between terms is not
constant.
Determine whether each sequence is arithmetic.
a. 2, 4, 8, 10, 12, ...
Answer: This is not an arithmetic sequence because the
difference between terms is not constant.
b.
Answer: This is an arithmetic sequence because
the difference between terms is constant.
Find the next three terms of the arithmetic sequence.
–8, –11, –14, –17, ...
Find the common difference
by subtracting successive terms.
–8
–11
–14
–17
–3
–3
–3
The common difference is –3.
Add –3 to the last term of the sequence to get the next term
in the sequence. Continue adding –3 until the next three
terms are found.
–17
–20
–3
–23
–3
–26
–3
Answer: The next three terms are –20, –23, –26.
Find the next three terms of the arithmetic sequence.
5, 12, 19, 26, ...
33, 40, 47
Find the 9th term of the arithmetic sequence.
7, 11, 15, 19, ...
In this sequence, the first term, a1 , is 7. You want to find the
9th term,
Find the common difference.
7
11
+4
15
+4
19
+4
The common difference is 4.
Use the formula for the nth term of an arithmetic sequence.
Formula for the nth term
Simplify.
Answer: The 9th term in the sequence is 39.
Find the 12th term in the arithmetic sequence.
12, 17, 22, 27, ...
67
Consider the arithmetic sequence –8, 1, 10, 19, ....
Write an equation for the nth term of the sequence.
In this sequence, the first term, a1, is –8. Find the
common difference.
–8
1
+9
10
+9
19
+9
The common difference is 9.
Use the formula for the nth term to write an equation.
Formula for nth term
Distributive Property
Simplify.
Answer: An equation for the nth term in this sequence
is
.
.
Check
.
and so on.
Find the 12th term of the sequence.
Replace n with 12 in the equation written in part a.
Equation for the nth term
Replace n with 12.
Simplify.
Graph the first five terms of the sequence.
n
1
–8
(1, –8)
2
1
(2, 1)
3
10
(3, 10)
4
19
(4, 19)
5
28
(5, 28)
Notice the points fall on a line. The graph
of an arithmetic sequence is linear.
Consider the arithmetic sequence –3, 0, 3, 6, ...
a. Write an equation for the nth term of the sequence.