# Math -- nth term

What is nth term of 41?

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1. No idea.

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2. The nth term is generated when a growing pattern exits. Such as 4 toothpicks make a square, then add three more toothpicks to one side of the existing square to make another square, then three more toothpicks to make another attached square. The nth term would be found by the generating function. So fn = 3n + 4 where n is the number of times you lay down toothpicks and fn is the total number of toothpicks... so the 41st time you lay down toothpicks there are f(41) = 3(41) + 4 toothpicks.
Note: we could have also generated the number of squares that are produced at each step : )

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