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11.1 Mathematical Patterns

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Ex 1 Start with a square with sides 1 unit long. On the right side, add on a square of the same size. Continue adding one square at a time in this way. Draw the first four figures.

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Ex 2 Write the number of 1 unit segments in each figure from ex 1 as a sequence.

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Ex 3 Describe the pattern formed and find the next three terms. 243, 81, 27, 9, …

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Ex 4 Suppose you drop a ball from a height of 100 cm. It bounces back to 80% of its previous height. How high will it go after its fifth bounce?

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We can use a variable with positive integer subscripts to represent the terms in a sequence: a 1 a 2 a 3 – first, second and third terms a n-1: n – 1 term a n : nth term a n+1: n + 1 term n is the term number

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Recursive formula Defines the terms in a sequence by relating each term to the ones before it. (ex 4 was recursive b/c the height was 80% of its previous height) Formula would be a n = 0.80a n-1 where a 1 = 100

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Ex 5 Describe the pattern of the sequence: 2, 6, 18, 54, 162, … Write a recursive function. Find the 6 th and 7 th terms. Find the value of a 10

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Explicit formula Expresses the nth term in terms of n Finding the value of a term without knowing the preceding term. (Find a link between the term number and the term value.)

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EX 6 Write a formula. 2, 6, 12, 20, …

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Ex 7 Write a formula 3, 5, 7, 9, …

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Ex 8 Terma 1 a 2 a 3 a 4 Length of side1234 perimeter perimeter For each sequence, find the next term and the 20 th term. Write an explicit formula for each sequence. n = the term number

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Ex 9 Write the first six terms of the area of squares that have side lengths 1, 2, 3, etc. Write an explicit formula.

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Ex 10 Write a formula for

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Ex 11 Write a formula for:

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