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Geometric Mean and Radicals Keystone Geometry

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Sequences 2 Arithmetic Sequence: Is a pattern of numbers where any term (number in the sequence is determined by adding or subtracting the previous term by a constant called the common difference. Geometric Sequence: Is a pattern of numbers where any term (number in the sequence) is determined by multiplying the previous term by a common factor. Example:2, 5, 8, 11, 14, ____, ____, ____ 17 20 23 Common difference = 3 Example:2, 6, 18, 54, 162, _____, _____, ____486 1458 4374 Common Factor = 3

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Examples 3 1. Starting with the number 1 and using a factor of 4, create 5 terms of a geometric sequence. 1, 4, 16, 64, 256 2. Starting with the number 2 and using a factor of 5, create 5 terms of a geometric sequence. 2, 10, 50, 250, 1250 3. Starting with the number 5 and using a factor of 3, create 5 terms of a geometric sequence. 5, 15, 45, 135, 405 4. Find the missing term in the geometric sequence 2, ____, 72, 432… 12 5. Find the missing term in the geometric sequence 6, ____, 24,... 12

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Geometric Mean 4 A term between two terms of a geometric sequence is the geometric mean of the two terms. Example: Find the geometric mean of 3 and 300. In the geometric sequence 4, 20, 100, ….(with a factor of 5), 20 is the geometric mean of 4 and 100. Try It: 3, ___, 300 30

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Geometric Mean : Fact 5 Consecutive terms of a geometric sequence are proportional. Example:Consider the geometric sequence with a common factor 10. 4, 40, 400 cross-products are equal (4)(400) = (40)(40) 1600 = 1600

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Therefore ……….. 6 To find the geometric mean between 7 and 28... 7, ___, 28label the missing term x write a proportion cross multiply solve

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7 Try It:Find the geometric mean of... 1. 10 and 40 Answer = 20 2. 1 and 36 Answer = 6 3. 10 and 20 Answer = 14.14 4. 5 and 6 Answer = 5.48 5. 8.1 and 12.2 Answer = 9.94 The geometric mean between two numbers a and b is the positive number x where. Therefore x =

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