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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