2004 AMC 12A Problem 14
Problem 14 of 25IntermediateAlgebra
A sequence of three real numbers forms an arithmetic progression with a first term of If is added to the second term and is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term of the geometric progression?
Answer choices
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Solution
The arithmetic progression is After the additions, the geometric progression is
The geometric condition gives which simplifies to so or
The corresponding third terms are and so the smallest possible value is
Thus, the correct answer is A.