Page 227 - Algebra 1

The first term of a sequence is denoted as a1, the second term as a2, the third term a3, and so on. The nth term of an arithmetic sequence is denoted an. The term preceding an is denoted an-1. For example, if n = 6, then the term preceding a6 is a6-1 or a5.
Term Number (n)
Term
Sequence Pattern
Description
1
1st or a1
7
a1
2
2nd or a2
(7) + 4
a1 + d
3
3rd or a3
(7 + 4) + 4
a2 + d
4
4th or a4
(7 + 4 + 4) + 4
a3 + d
5
5th or a5
(7 + 4 + 4 + 4) + 4
a4 + d
n
nth or an
an-1 + 4
an - 1 + d
Math Reasoning
Generalize Give an example of an arithmetic sequence. State the first 4 terms and the common difference.
Arithmetic sequences can be represented using a formula.
Arithmetic Sequence Formula
Use the formula below to find the next term in a sequence. an =an-1 +d
a1 = first term
d = common difference n = term number
In the arithmetic sequence 7, 11, 15, 19, ..., a1 = 7, a2 = 11, a3 = 15, and a4 = 19. The common difference is 4.
Example
2
Using a Recursive Formula
Use a recursive formula to find the first four terms of an arithmetic sequence where a1 = -2 and the common difference d = 7.
212 Saxon Algebra 1
SOLUTION
an =an-1 +d an =an-1 +7
a1 = -2
a2 = -2 + 7 = 5
a3 = 5 + 7 = 12
a4 = 12 + 7 = 19
Write the formula. Substitute 7 for d. Write the first term. Find the second term. Find the third term. Find the fourth term.
The first four terms of the sequence are -2, 5, 12, and 19.
A rule for finding any term in an arithmetic sequence can be developed by looking at a different pattern in the sequence 7, 11, 15, 19, ....