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jmc

algebra senior

Problem

By starting with a million and alternatively dividing by 2 and multiplying by 5, Anisha created a sequence of integers that starts 1000000, 500000, 2500000, 1250000, and so on. What is the last integer in her sequence? Express your answer in the form , where and are positive integers and is as small as possible.
Solution
Anisha begins with the integer . After 12 steps, every factor of 2 is removed and replaced with a factor of , so what remains is .
Final answer
5^{12}