1.2 Mathematical Patterns Warm-up Page 11 #13 How are expressions written and graphed for arithmetic patterns?

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1.2 Mathematical Patterns Warm-up Page 11 #13 How are expressions written and graphed for arithmetic patterns?

Introduction to Arithmetic Sequences

Definition of a Sequence  A sequence is an ordered list of numbers.  Each number in the list is called a term of the sequence.  Infinite sequence has an infinite number of terms. First term is u 1 Nth term is u n Term before is u n-1  Graph of sequence is a scatterplot of ordered pairs (term #, terms from set) How are expressions written and graphed for arithmetic patterns?

Example  Find the next two terms in the sequence. Graph the sequence. How are expressions written and graphed for arithmetic patterns?

Practice Page 19 #1

Recursively Defined Sequence  First term is given and there is a method of determining the nth term by using the terms that precede it.  Example: How are expressions written and graphed for arithmetic patterns?

Calculator Tips  Select Mode  Arrow down to “Func Par Pol Seq”  Arrow over to Seq and select enter to make it dark. How are expressions written and graphed for arithmetic patterns?

Application Example 1  A basketball is dropped from a height of 8 feet. It hits the floor and bounces to a height of 6 feet. It continues to bounce, and on each rebound it rises to ¾ the height of the previous bounce. Write a recursive formula for this problem. Find the height of the ball on the fifth bounce. How are expressions written and graphed for arithmetic patterns?

Application Example 2  Rick owns an automobile dealership. Last year, he spent $16,000 on advertising. He plans to increase his advertising expenditures by $1200 this year and in each subsequent year. What will be the amount he spends on advertising in the sixth year? How are expressions written and graphed for arithmetic patterns?

Application Example 3  Ms. Long creates an endowment fund for her alma mater. She places $250,000 in the fund to start, and will add $50,000 to the fund each year. She states that 25% of the total amount shall be used each year for scholarships. How much will be in the fund at the end of the sixth year? How are expressions written and graphed for arithmetic patterns?

Practice: Pages #9,13,17 Homework: Pages #2-20 even How are expressions written and graphed for arithmetic patterns?

Ticket out the door…  What is a recursive formula?