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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=−43a_1 = -43\newlinean=an−1−11a_n = a_{n - 1} - 11\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=−43a_1 = -43\newlinean=an−1−11a_n = a_{n - 1} - 11\newlinean=_a_n = \_
  1. Identify Sequence Type: We got a1=−43a_1 = -43 and an=an−1−11a_n = a_{n-1} - 11, which means it's an arithmetic sequence with a common difference of −11-11.
  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: Plug in a1=−43a_1 = -43 and d=−11d = -11 into the formula: an=−43−11(n−1)a_n = -43 - 11(n - 1).
  4. Simplify Formula: Simplify the formula: an=−43−11n+11a_n = -43 - 11n + 11.
  5. Combine Like Terms: Combine like terms: an=−11n−32an = -11n - 32.

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