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Lesson 1

1. Lesson 1

1.10. Explore 6

Mathematics 20-1 Module 1

Module 1: Sequences and Series

 

General Term of the Sequence
 

From working through Try This 4, you may have discovered that you can find the value of any term in an arithmetic sequence by using the formula tn = a + (n − 1)d.

 

This formula is called the general term of the sequence. As with any formula, if you are given values for all but one variable, you will be able to solve the equation for the unknown variable. In the remainder of the lesson you will use the general term to determine tn, a, n, and d.



formula

Throughout this course you will learn many formulas for solving problems. Use the document Formula Sheet, or a tool recommended by your teacher, to keep track of these formulas. You will use Formula Sheet to review all of the formulas at the end of each module and to prepare for your final assessment.

 

course folder Save Formula Sheet in your course folder now.

 

You will update this document throughout Mathematics 20-1. For now, add the formula for the general term of the sequence to your copy of Formula Sheet.

 

Share 2
 

Retrieve your results from Try This 1. In that activity you studied arrangements of marbles in three figures, as shown in the illustration. You discovered a pattern and used that pattern to determine the number of marbles in subsequent arrangements.

 

This is an illustration of three arrangements of marbles. The first arrangement has 10 marbles. The second arrangement has 14 marbles. The third arrangement has 18 marbles.

 

You used a method for determining the number of marbles in figure 20 and in figure 100. If possible, work with a partner on the following questions, and then share your work with a group.

  1. If t1 = 10 marbles, t2 = 14 marbles, t3 = 18 marbles, and so on, what is the value of tn if n is the figure number? (In other words, construct a formula that will allow you to find the number of marbles in any given figure.)

  2. Share your formulas with other groups. Record any formulas that are different from yours. Verify that these formulas will lead to the correct answer.

  3. With your partner, evaluate the advantages and disadvantages of each of the formulas you have learned. Be sure to talk about

     

    • the complexity of the formula

    • the variables required in each formula

    • the ability to use the formula for both small and large values of n.

course folder If required, save a copy of your discussion in your course folder.