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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 on theme: "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."— Presentation transcript:

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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?

4 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?

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

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

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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.

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

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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.

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Types of a “Sequence”?

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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)

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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, the common ratio is 4. (each term is arrived at through multiplication)

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14 How to find the Common Ratio

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