Lesson 1
1. Lesson 1
1.11. Explore 7
Module 1: Sequences and Series
Example 3
Work through Dakota’s Example. The general term of the sequence formula will be used to help solve the problem. You might recognize the question from the beginning of Explore.
Self-Check 2
Assume that, at age 17, Dakota gets a part-time job earning $12/h. He receives a signing bonus of $250 when he begins his job.
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- Complete the table relating Dakota's earnings to the number of hours worked.
Number of Hours Worked Earnings ($) 0 250 1 262 2 3 4 5
- Identify the a and d in the arithmetic sequence represented by the earnings column. Answer
Be careful when you establish the value of a. Remember that a is the same as t1. What do you want t1 to represent in this problem?
- Write the general term representing this situation. Answer
- Show how you would use the general term to determine the number of hours Dakota needs to work to earn $1270. Answer
Go to the textbook for additional examples demonstrating how you can use the general term to determine properties of an arithmetic sequence. Turn to page 10 to view “Example 1.” Look at “Method 1” only. Then turn to page 12 to view “Example 2.” Work through each example and pay attention to
- where given values in the problem are substituted into the formula
- the difference between how you should interpret n versus tn
Compare the solution strategies demonstrated in the textbook examples to Example 3, which you looked at in the video about Dakota's earnings.
In your course folder, write down the points the textbook examples have added to your understanding of arithmetic sequences.
Self-Check 3
Use Arithmetic Sequences Mini-Quiz to check your understanding of arithmetic sequences.