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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=25a_1 = 25\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=25a_1 = 25\newlinean=an−1−7a_n = a_{n - 1} - 7\newlinean=_a_n = \_
  1. Identify Arithmetic Sequence: We got a1=25a_1 = 25 and an=an−1−7a_n = a_{n - 1} - 7, so it's like 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. Plug in Values: Plug in a1=25a_1 = 25 and d=−7d = -7 into the formula: an=25−7(n−1)a_n = 25 - 7(n - 1).
  4. Simplify Expression: Now simplify it: an=25−7n+7a_n = 25 - 7n + 7.
  5. Combine Like Terms: Combine like terms: an=32−7nan = 32 - 7n.

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