Sequence: A list of numbers in a particular order Term- Each number in the sequence is called a term Arithmetic sequence- is a sequence in which each term after the first is found by adding a constant, called the common difference Ex. 3, 7, 11, 15, 19, 23……. a1 = 3 a2 = 7 a3 = 11……

An arithmetic sequence has a common difference between consecutive terms.

Find the next four terms of the arithmetic sequence –8, –6, –4, …. Find the common difference d by subtracting 2 consecutive terms. Now add 2 to the third term of the sequence and then continue adding 2 until the next four terms are found. +2 +2 +2 +2 –4 –2 0 2 4 Answer: The next four terms are –2, 0, 2 and 4. Example 1-1a

Construction The table below shows typical costs for a construction company to rent a crane for one, two, three, or four months. Assuming that the arithmetic sequence continues, how much would it cost to rent the crane for 24 months? Months Cost($) 1 75,000 2 90,000 3 105,000 4 120,000 Example 1-2a

Months Cost($) 1 75,000 2 90,000 3 105,000 4 120,000 Explore Since the difference between any two successive costs is $15,000, the costs form an arithmetic sequence with common difference 15,000. Plan You can use the formula for the nth term of an arithmetic sequence with and to find the cost for 24 months. Example 1-2a

Formula for the nth term Solve Formula for the nth term Simplify. Answer: It would cost $420,000 to rent for 24 months. Example 1-2a

Examine. You can find the term of the sequence by adding 15,000 Examine You can find the term of the sequence by adding 15,000. From Example 2 on page 579 of your textbook, you know the cost to rent the crane for 12 months is $120,000. So, a12 through a24 are 240,000, 255,000, 270,000, 285,000, 300,000, 315,000, 330,000, 345,000, 360,000, 375,000, 390,000, 405,000, and 420,000. Therefore, $420,000 is correct. Example 1-2a

In this sequence, and Use the nth formula to write an equation. Write an equation for the nth term of the arithmetic sequence –8, –6, –4, …. In this sequence, and Use the nth formula to write an equation. Formula for the nth term Distributive Property Simplify. Answer: An equation is . Example 1-3a

Find the three arithmetic means between 21 and 45. You can use the nth term formula to find the common difference. In the sequence 21, ___, ___, ___, 45, ..., and Formula for the nth term Subtract 21 from each side. Divide each side by 4. Example 1-4a

Now use the value of d to find the three arithmetic means. +6 +6 +6 21 27 33 39 Answer: The arithmetic means are 27, 33, and 39. Check Example 1-4a

End of Lesson 1