Lesson 3

Using the Sn Formulas to Evaluate Other Properties of Arithmetic Series

 

Besides using the two series formulas to evaluate the sum of arithmetic series, you can also use the formulas to evaluate other properties of arithmetic series. Just as you were able to use the general term tn = a + (n − 1)d to evaluate tn, a, n, and d, you can also determine all of these properties using the series formulas.

 

Example

 

Use Building an Obstacle Course to solve a problem that uses the series formulas. Pay attention to how the information provided is used to determine which formula to use.

Try This 4

 

You have seen an example of how you can use the Sn formulas to determine the properties of an arithmetic series. Apply what you have learned to the next problem, which is based on the same context as the example.

 

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Problem

 

An obstacle course uses 10 log stumps. All of the logs are cut from a single log that measures 7.7 m. The difference in height between consecutive log stumps is 0.1 m. Determine the height of the shortest stump. Show your work and record each step of your solution.

 

Save your work in your course folder.

 

Share 3

1. Compare your answers with those of a classmate. There are different ways of solving this problem. Keep the following points in mind as you discuss your solutions:
   
   
   • Do your solutions match? If not, work together to identify the error(s).
     
     
   • How are your approaches different? If they are different, what are the pros and cons of each method?
     
     
2. Work with your classmate to find the height of the tallest stump. Try to find at least two approaches to solving this problem.

Save your answers in your course folder.

 

Your teacher may want to look at your work to see how your collaboration with your classmate(s) has affected your learning.