What Is A Function



Activity 11.1 Arithmetic Series

Overview:

This activity is a worksheet that explores the number of seats in a theater, which can be modeled by an arithmetic series. The worksheet leads students through the process of finding the formula of the series by asking a series of directed questions. Students are then asked to identify which of four given series are arithmetic.

Estimated Time Required:

The activity should take approximately 20 minutes.

Technology: None

Concepts:

• Arithmetic series and the associated notation

Discussion:

When you generalize the structure of an arithmetic sequence, use caution in introducing the standard notation that uses subscripts.

Activity 11.1 Arithmetic Series

1. Suppose a theater has 40 rows of seats; the first row contains 18 seats, and the number of seats increases by 2 per row. How many seats are in the theater?

To answer this question (without adding up every single term), work through the following steps:

a.) Write a sequence for the number of seats in consecutive rows, starting with 18 (the first row)

b.) Now, write out the sum you are trying to find (use … in the middle to save space).

c.) By pairing the first and last term, the second and next-to-last term, and so on, do you notice a pattern? How many seats are in the theater?

d.) Now, find a formula for determining the number of seats in the nth row.

e.) Can you relate the sum you found in part (c) to your formula in part (d) to find a general formula for the sum of the first n terms of this type of sequence?

2. Which of the following sequences are arithmetic?

a.) [pic] b.) [pic] c.) [pic]

d.) [pic]

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