MathDB
Problem: 2004 AMC 10 #18

Source:

February 1, 2007
quadraticsarithmetic sequencegeometric sequencegeometric series

Problem Statement

A sequence of three real numbers forms an arithmetic progression with a first term of 9 9. If 2 2 is added to the second term and 20 20 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? <spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 36<spanclass=latexbold>(D)</span> 49<spanclass=latexbold>(E)</span> 81 <span class='latex-bold'>(A)</span>\ 1\qquad <span class='latex-bold'>(B)</span>\ 4\qquad <span class='latex-bold'>(C)</span>\ 36\qquad <span class='latex-bold'>(D)</span>\ 49\qquad <span class='latex-bold'>(E)</span>\ 81