Maths Olympiad Prep

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Algebra Difficulty 4.8 AIME Find the answer

Some terms are deleted from an infinite arithmetic progression 1,x,y,1, \mathrm{x}, \mathrm{y}, \ldots of real numbers to leave an infinite geometric progression 1,a,b,1, \mathrm{a}, \mathrm{b}, \ldots. Find all possible values of a.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

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