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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=19a_1 = 19\newlinean=an−1−8a_n = a_{n - 1} - 8\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=19a_1 = 19\newlinean=an−1−8a_n = a_{n - 1} - 8\newlinean=_a_n = \_
  1. Identify Sequence Type: Initial term is a1=19a_1 = 19, and the recursive formula is an=an−1−8a_n = a_{n - 1} - 8. This looks like an arithmetic sequence with a common difference of −8-8.
  2. Find Common Difference: The common difference dd in the recursive formula an=an−1−8a_n = a_{n - 1} - 8 is −8-8.
  3. Apply Explicit Formula: The explicit formula for an arithmetic sequence is an=a1+d(n−1)a_n = a_1 + d(n - 1). We plug in a1=19a_1 = 19 and d=−8d = -8.
  4. Substitute Values: Substitute the values into the formula: an=19−8(n−1)a_n = 19 - 8(n - 1).
  5. Simplify Formula: Simplify the formula: an=19−8n+8a_n = 19 - 8n + 8.
  6. Combine Like Terms: Combine like terms: an=27−8nan = 27 - 8n.

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