Lesson 5: 3-6 Arithmetic Sequences as Linear Functions

How do you determine each next term in an arithmetic sequence?

arithmetic sequence

F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

SAT questions related to slope: 8-3-13,6-3-1,5-4-7,8-3-19,7-4-17,1-3-6,3-4-8;
graphing: 6-3-5;
functions: 3-4-4, 5-4-2, 6-4-25

A sequence is a set of numbers in a specific order. The numbers in a sequence are called terms. If the terms of a sequence increase or decrease at a constant rate, it is called an arithmetic sequence. The difference between successive terms of an arithmetic sequence is called the common difference.

The arithmetic sequence 12, 23, 34, 45 … represents the total number in ounces that a bag weighs after each additional newspaper is added.

a. Write a function to represent this sequence.

b. Graph the function and determine the domain.

Make sure students carefully keep track of the variables in the function an = a1 + (n - 1)d as it is easy to substitute for the wrong variable when using this function.

If students have an interest in nature, then share that sequences are often visible in nature. Have students take photographs or find pictures in magazines or on calendars of examples of sequences in nature. One such example is the sequence found in the arrangement of seeds in a daisy. This particular sequence is called the Fibonacci sequence.

Practice: Exercises 1- 7

Exercises 37 - 43

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