Lesson 6

Are You Ready?

Before beginning this lesson you should be able to

• convert decimals to reduced fractions
  
  
• define terms related to sequences and series
  
  
• solve problems involving geometric sequences

Complete these questions. If you experience difficulty and need help, visit Refresher or contact your teacher.

1. Complete a table like this one by converting each of the following decimals into fractions in the form Reduce to the simplest form where possible.
   
   
    

   Decimal	Fraction
   0.3
   3.78
   0.012

   
   
   Answer
   
   
2. Identify the difference between each of the following terms.
   
   
   1. an arithmetic sequence and a geometric sequence Answer
      
      
   2. an infinite sequence and a finite sequence Answer
      
      
   3. a sequence and a series Answer
      
      

3. Consider the geometric sequence 5, 10, 20, 40, ….

   
   
   1. Determine the general term tn. Answer
      
      
   2. Calculate t10. Answer
      
      
   3. Determine S10 for the corresponding geometric series. Answer
      
      
4. Define the word “infinite.” Give an example of something that is infinite. Answer
   

How did the questions go? Depending on your answer, skip forward to Discover or work through Refresher.