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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=−18a_1 = -18\newlinean=an−1−13a_n = a_{n - 1} - 13\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=−18a_1 = -18\newlinean=an−1−13a_n = a_{n - 1} - 13\newlinean=_a_n = \_
  1. Initial Term: The initial term is a1=−18a_1 = -18.
  2. Recursive Formula: The recursive formula is an=an−1−13a_n = a_{n - 1} - 13. This means each term is 1313 less than the previous term.
  3. Explicit Formula: To find the explicit formula, we need to express ana_n in terms of nn using the initial term and the common difference.
  4. Arithmetic Sequence: The sequence is arithmetic with a common difference of −13-13. The explicit formula for an arithmetic sequence is an=a1+(n−1)da_n = a_1 + (n - 1)d.
  5. Substitute Values: Substitute a1=−18a_1 = -18 and d=−13d = -13 into the formula: an=−18+(n−1)(−13)a_n = -18 + (n - 1)(-13).
  6. Simplify Formula: Simplify the formula: an=−18−13n+13a_n = -18 - 13n + 13.

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