Lesson 2

Lesson 2 Summary

 

In this lesson you investigated the following questions:

• How are arithmetic sequences related to linear functions?

• How are sequences useful in solving problems?

You continued your study of arithmetic sequences. You investigated how arithmetic sequences are related to linear functions. By investigating the properties of an Archimedes' Spiral you found that arithmetic sequences are linear functions whose domains are restricted to natural numbers.

 

As a result, the graph comparing the term value to the position of the term is linear. Connecting the points in these graphs is inappropriate since points along the graph that are between two consecutive terms are meaningless.

 

You also analyzed situations that can be modelled by arithmetic sequences. You practised using arithmetic sequences to solve problems involving part-time earnings and investing for simple interest. You studied patterns and constructed tables and graphs to develop equations and formulas that described the context.

 

You learned that such contexts can be described by the linear equation y = mx + b and by the general term tn = a + (n − 1)d. You used those formulas and equations to solve other problems. By summarizing a pattern in the form of an equation, you can predict future behaviour.

 

In the next lesson you will continue your study of sequences by focusing on adding the terms of an arithmetic sequence.