Consider the pattern 10, x, 40, . . . a. If the pattern is an arithmetic sequence, the
Chapter 11, Problem 19(choose chapter or problem)
Consider the pattern 10, x, 40, . . . a. If the pattern is an arithmetic sequence, the value of x is called the arithmetic mean of 10 and 40. Use your algebra skills to explain how to calculate the arithmetic mean of any two numbers. b. If the pattern is a geometric sequence, the positive value of x is called the geometric mean of 10 and 40. Use your algebra skills to explain how to calculate the geometric mean of any two positive numbers. c. For any two positive numbers, the ratio of the smaller number to their geometric mean is equal to the ratio of the geometric mean to the larger number. Find the formula for the geometric mean of a and b by solving the proportion for c. Are there any values for which this formula isnt true? d. Use this formula to find the geometric mean of 2 and 50, and of 4 and 36.
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