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  1. Let \(t_n\) be the number of toothpicks required to make a size \(n\) triangular grid. Write out the first 5 terms of the sequence \(t_1, t_2, \ldots\text{.}\)

  2. Find a recursive definition for the sequence. Explain why you are correct.

  3. Is the sequence arithmetic or geometric? If not, is it the sequence of partial sums of an arithmetic or geometric sequence? Explain why your answer is correct.

  4. Use your results from part (c) to find a closed formula for the sequence. Show your work.

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