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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=−33a_1 = -33\newlinean=an−1−7a_n = a_{n - 1} - 7\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=−33a_1 = -33\newlinean=an−1−7a_n = a_{n - 1} - 7\newlinean=_a_n = \_
  1. Initial Term and Recursive Formula: Initial term is a1=−33a_1 = -33. Recursive formula is an=an−1−7a_n = a_{n - 1} - 7. This is an arithmetic sequence with a common difference of −7-7.
  2. Explicit 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 a1=−33a_1 = -33 and d=−7d = -7 into the formula.an=−33+(−7)(n−1).a_n = -33 + (-7)(n - 1).
  4. Simplify Formula: Simplify the formula. an=−33−7n+7a_n = -33 - 7n + 7.
  5. Combine Like Terms: Combine like terms. an=−7n−26an = -7n - 26.

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