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Consider the sequence \(5, 9, 13, 17, 21, \ldots\) with \(a_1 = 5\)

  1. Give a recursive definition for the sequence.

  2. Give a closed formula for the \(n\)th term of the sequence.

  3. Is \(2013\) a term in the sequence? Explain.

  4. How many terms does the sequence \(5, 9, 13, 17, 21, \ldots, 533\) have?

  5. Find the sum: \(5 + 9 + 13 + 17 + 21 + \cdots + 533\text{.}\) Show your work.

  6. Use what you found above to find \(b_n\text{,}\) the \(n^{th}\) term of \(1, 6, 15, 28, 45, \ldots\text{,}\) where \(b_0 = 1\)

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