Problem Solving Skills for Mathcounts Competitions
Book Store => Bookstore => Twenty Mock Mathcounts Sprint Round Practices => Topic started by: wxc0212 on February 10, 2011, 10:26:01 PM
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While doing some practice questions my mom printed out for me i ran accross a question that i wasn't able to figure out.
Here's the question:
A positive number has a decimal part and an integer part. The decimal part, the integer part, and the positive number itself form a geometric sequence. Find this positive number.
Could someone please help. Thank you!
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It is a hard problem. There are some hints in the answer key page for this problem.
Let a be the integer part of the number and b be the decimal part. The number can then be written as a + b.
Since the three terms of b, a, and a+b form a geometric sequence, the following equation is true: a^2 = b(b+a).
Dividing both sides of the equation by a^2 you will get another equation.
Following the steps as shown in page 8 of the book, you will get the final result.
Good luck!