# 8/9/2009 Finding the nth term Applying a rule to find any term

```8/9/2009
Finding the nth term
Lesson 1.4
Applying a rule to find any term
 When you are looking for a term (say the 20th term in a sequence) you do not
need to go through the first 19 to find the 20th if you know the rule.
 For example, suppose the rule is 4x-3. The variable x represents the term and
the answer is the value. Applying a rule is sometimes called a function. So if we
are looking for the 10th term, it would be 4(10) – 3 or 37.
 A table showing the first 10 terms would look like this:
Term
1
2
3
4
5
6
7
8
9
10
Value
1
5
9
13
17
21
25
29
33
37
Linear Function
 Rules that generate sequences with a common difference between terms are
called linear functions. The graph of the sequence always forms a line.
 Graph the sequence 3, 7, 11, 15, 19, 23, 27 . This sequence has 7 terms. The
ordered pairs are (term, value): (1,3) (2,7) (3,11) (4,15) (5,19) (6,23)(7,27).
35

30

25
20
15
10
x
5
1
2
3
4
5
6
7
1
```