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2011/12 AHSMC Part 1 Problem 6

Problem 6 of 16

Let x1,x2,…x_1, x_2, \ldots be a sequence of positive rational numbers such that x1=16x_1 = 16, x2=32x_2 = 32 and xn=xn−1+xn−22x_n = \frac{x_{n-1} + x_{n-2}}{2} for all positive integers n≥3n \ge 3. Then the value of x6x_6 is

Answer choices

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Solution

We have x3=24x_3 = 24, x4=28x_4 = 28, x5=26x_5 = 26, x6=27x_6 = 27 and x7=532x_7 = \frac{53}{2}. The answer is (D).

University of Alberta