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# The terms of a particular sequence are determined according to the following rules: * If the value of a given term is an odd positive intege

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The terms of a particular sequence are determined according to the following rules:
* If the value of a given term is an odd positive integer s, then the value of the following term is 3s-9
* If the value of a given term is an even positive integer l, then the value of the following term is 2t-7.
Suppose that the terms of the sequence alternate between two positive integers (a, b, a, b, ...). What is the sum of the two positive integers?

Mar 22, 2019

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$$\text{suppose }a \text{ is odd}\\ b = 3a-9\text{ is even}\\ a = 2(3a-9)-7 = 6a-25\\ 5a=25\\ a=5,~b = 6,~a+b=11$$

$$\text{suppose }a \text{ is even}\\ b = 2a-7\text{ is odd}\\ a = 3(2a-7)-9= 6a-30\\ 5a=30\\ a=6,~b=5,~a+b=11$$

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Mar 23, 2019