Lesson 4

Go to the textbook to see how you can use either logical reasoning or the general term to solve a problem related to geometric sequences. On pages 36 to 37, work through “Example 3.” This problem is different from what you have already encountered because you are given neither the first term nor the common ratio. Instead, these are the very values that you are required to find! Which method do you like better? What other variations are there for solving the problem?

Try This 6

You have derived and applied the general term tn = arn−1 to solve problems involving geometric sequences. What is the key characteristic of geometric sequences? Try This 6 challenges your understanding of geometric sequences.

Your task is to solve the problem. Think about the problem, and then try one or more ways of solving the problem. If you get stuck, ask for a hint.

Three terms of a geometric sequence are x + 4, x, x − 3. Determine the value of each term.

Save your responses in your course folder.

Share 3

With a partner, compare and discuss your solutions. Use the following questions as a guide for your discussion.

1. What is the key understanding that is required to solve this type of problem?
   
   
2. Is the common ratio greater than 1 or less than 1? How could you have determined the answer to this question without solving for r?
   
   
3. Compare your method with your partner’s method. In what ways are your methods similar? In what ways are your methods different? Are the methods based on the same key principles?
   
   
4. In what ways can you verify that you have the correct solution?

Save your responses in your course folder.

Self-Check 3

Complete questions 9, 14, 23, and 25 on pages 40 to 44 of the textbook. Remember to show your work and review parts of this lesson if you need to. Answers