Lesson 1
1. Lesson 1
1.8. Explore 4
Module 1: Sequences and Series
Algebraic Method
Even with a calculator, repeated calculations may not be very efficient, especially if you were asked to determine the value of a term that is far into the sequence. That’s where an algebraic method helps.
You can use an algebraic method to identify specific terms in an arithmetic sequence. In Try This 4 you will develop a formula for evaluating arithmetic sequences.
When working with arithmetic sequences, you will encounter and use terms that describe the sequence’s properties. These variables include the following:
Variable |
Meaning |
a |
the first term in the sequence (or t1) |
d |
the common difference |
n |
the position of the term in the sequence |
tn |
the value of the nth term |
You can use the variable tn to refer to any term in the sequence. Here are some examples:
- If you are solving for the third term in a sequence, simply replace the n in tn with the number 3. So, t3.
- If you are solving for the 10th term, simply replace the n in tn with the number 10. So, t10.
If you are solving for the 150th term, what variable could you use to refer to this term? 
Look at the definition of Sequence. Compare this definition with the one you already added to your copy of Module 1 Glossary Terms. You may want to revise or add to your definition. Scroll down through Sequence and read the “More” section.
As you read the definition, pay particular attention to the following:
- What is the difference between a finite sequence and an infinite sequence?
- How is the tn notation used?
- How do you use notation to distinguish finite and infinite sequences?
Add what you have learned about finite and infinite sequences to Module 1 Glossary Terms.
Self-Check 1
Refer to the definitions of the variables a, d, n, and tn to answer the following questions.
Consider the sequence 20, 18, 16, 14, 12, 10, 8.