2020 AIME I Problems/Problem 2
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Problem
There is a unique positive real number such that the three numbers , , and , in that order, form a geometric progression with positive common ratio. The number can be written as , where and are relatively prime positive integers. Find .
Solution
Since these form a geometric series, is the common ratio. Rewriting this, we get by base change formula. Therefore, the common ratio is 2. Now . Therefore, .
~ JHawk0224
See Also
2020 AIME I (Problems • Answer Key • Resources) | ||
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Followed by Problem 3 | |
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