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math problem

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Several months ago, Deven bought two plants. The two plants had the same height at the time when they were purchased. Ever since then, Plant A grew $$20$$ centimeters every month. Plant B grew 1 centimeter in the first month after its purchase, 2 centimeters in the following month, and generally grew n centimeters in the nth month after its purchase. Deven finds out today that the two plants have the same height again. How many months ago did he buy the two plants?

Mar 6, 2022

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Write it as an equation: $$20m= {m(m+1) \over 2}$$

The first term is the height of the first plant, and the second term is the sum of an arithmatic series that represents the height of the second plant.

Solving, we find it took $$\color{brown}\boxed{39}$$ months

Mar 6, 2022