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Use the initial term and the recursive formula to find an explicit formula for the sequence ana_n. Write your answer in simplest form.\newlinea1=−29a_1 = -29\newlinean=an−1+4a_n = a_{n - 1} + 4\newlinean=_____a_n = \_\_\_\_\_

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Q. Use the initial term and the recursive formula to find an explicit formula for the sequence ana_n. Write your answer in simplest form.\newlinea1=−29a_1 = -29\newlinean=an−1+4a_n = a_{n - 1} + 4\newlinean=_____a_n = \_\_\_\_\_
  1. Identify Sequence Type: Initial term is a1=−29a_1 = -29, and the recursive formula is an=an−1+4a_n = a_{n-1} + 4. This looks like an arithmetic sequence with a common difference of 44.
  2. Arithmetic Sequence Formula: The explicit formula for an arithmetic sequence is an=a1+d(n−1)a_n = a_1 + d(n - 1), where dd is the common difference.
  3. Substitute Values: Substitute the given values into the formula: an=−29+4(n−1)a_n = -29 + 4(n - 1).
  4. Simplify Formula: Simplify the formula: an=−29+4n−4a_n = -29 + 4n - 4.
  5. Combine Like Terms: Combine like terms: an=4n−33an = 4n - 33.

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