How many tiles did he add? INTRO TO SEQUENCES AND SERIES Guido wants to create a tile mosaic around the Ram-Fountain. In the first week he begins.

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Presentation transcript:

How many tiles did he add? INTRO TO SEQUENCES AND SERIES Guido wants to create a tile mosaic around the Ram-Fountain. In the first week he begins his work by placing red tiles around the fountain as shown: How many tiles did he add?

How many tiles did he add? In the second week, he adds to his work by placing purple tiles around the fountain as shown: How many tiles did he add?

How many tiles did he add? In the third week, he adds to his work by placing green tiles around the fountain as shown: How many tiles did he add?

INTRO TO SEQUENCES AND SERIES If he continues this pattern, how many blue tiles will he need to complete his fourth week of work?

INTRO TO SEQUENCES AND SERIES In the 10th week, how many tiles would you expect him to add. How many total are around the fountain? Explain how you arrived at this answer.

INTRO TO SEQUENCES AND SERIES What is a “Sequence”? A list of things (usually numbers) that are in order.

INTRO TO SEQUENCES AND SERIES What is an “Infinite Sequence”? An infinite sequence is a function whose domain is the set of positive integers. The function values a1, a2, a3, a4, a5, a6, a7. . . Are the terms of the sequence. If the domain of a function consists of the first n positive integers only, the sequence is a finite sequence A list of numbers separated by commas: 1, 2, 4, 8...., 128……… INTRO TO SEQUENCES AND SERIES What is a “Sequence”? A list of numbers separated by commas: 1, 2, 4, 8...., 128.

INTRO TO SEQUENCES AND SERIES Types of a “Sequence”?

INTRO TO SEQUENCES AND SERIES Types of a “Sequence”? Arithmetic: a sequence of numbers that has a common difference (d). EX: 1, 3, 5, 7 the common difference is 2. (each term is arrived at through addition)

INTRO TO SEQUENCES AND SERIES Types of a “Sequence”? Arithmetic: a sequence of numbers that has a common difference (d). EX: 1, 3, 5, 7 the common difference is 2. (each term is arrived at through addition) Geometric: a sequence of numbers that has a common ratio (r). EX: 3, 12, 48, 192 the common ratio is 4. (each term is arrived at through multiplication)

How to find the Common Ratio