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Presentation transcript:

All of these images have something in common.

Number Patterns (Sequences) A number pattern is also called a sequence. Each number in a sequence is called a term of the sequence. Today we will learn about a specific type of sequence: Arithmetic

Arithmetic Sequence 4, 8, 12, 16, 20, 24, ___, ___, ___ Do you see a pattern? If so, what are the next three terms?

Arithmetic Sequence +4 +4 +4 +4 +4 4, 8, 12, 16, 20, 24, 28, 32, 36 If there is a common difference between the terms then the sequence is an arithmetic sequence. This is an arithmetic sequence with a common difference of 4.

Arithmetic Sequence 6, 4, 2, 0, -2, -4, ___, ___, ___ Do you see a pattern? If so, what are the next three terms?

Arithmetic Sequence 6, 4, 2, 0, -2, -4, -6, -8, -10 -2 -2 -2 -2 -2 6, 4, 2, 0, -2, -4, -6, -8, -10 If there is a common difference between the terms then the sequence is an arithmetic sequence. This is an arithmetic sequence with a common difference of -2.

Arithmetic Sequence When is the next cable car due? On week days, between 6 am and 6 pm a cable car arrives at a certain spot at the following times: 6:14am, 6:28am, 6:42am, 6:56am, and the pattern continues. When is the next cable car due? The cable cars are 14 minutes apart, so the next is due at 7:10am.

Explicit Formula Formula used to find the nth term of a sequence

Explicit Formula for Arithmetic Sequence The difference between terms (the pattern) Term you are looking for

Find the common difference, the explicit formula, and the tenth term. 3, 9, 15, 21, … d = 6 an = 6n – 3 a10 = 57

Applications The marching band has 14 marchers in the front row, 16 in the second row, 20 in the fourth row, and so on. How many marchers are in the 15th row?

Applications Several friends want to go on a rafting trip. The cost of the trip per person is in the cart. How much would it cost for 9 people to go? Passengers 1 2 3 4 Cost $75 $100 $125 $150

Recursive Formula for Arithmetic Sequence The difference/ the pattern The term you are looking for

Find the first four terms of the sequence. Example: a1 = 3 an = an-1 + 2 3, 5, 7, 9

Write the recursive formula for the following sequence: 3,6,9,12… What are the next 3 terms?