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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=13a_1 = 13\newlinean=an−1−12a_n = a_{n - 1} - 12\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=13a_1 = 13\newlinean=an−1−12a_n = a_{n - 1} - 12\newlinean=_a_n = \_
  1. Identify Initial Term: Initial term is a1=13a_1 = 13, and the recursive formula is an=an−1−12a_n = a_{n - 1} - 12. This looks like an arithmetic sequence with a common difference of −12-12.
  2. Use Recursive Formula: To find the explicit formula for an arithmetic sequence, we use an=a1+(n−1)da_n = a_1 + (n - 1)d, where dd is the common difference.
  3. Apply Explicit Formula: Substitute the given values into the formula: an=13+(n−1)(−12)a_n = 13 + (n - 1)(-12).
  4. Simplify Formula: Simplify the formula: an=13−12(n−1)a_n = 13 - 12(n - 1).
  5. Distribute Common Difference: Distribute the −12-12: an=13−12n+12a_n = 13 - 12n + 12.

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