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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=5a_1 = 5\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=5a_1 = 5\newlinean=an−1+12a_n = a_{n - 1} + 12\newlinean=__a_n = \_\_
  1. Arithmetic Sequence Definition: Initial term is a1=5a_1 = 5 and recursive formula is an=an−1+12a_n = a_{n-1} + 12. This is an arithmetic sequence with a common difference of 1212.
  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. Substitution: Substitute a1=5a_1 = 5 and d=12d = 12 into the formula: an=5+12(n−1)a_n = 5 + 12(n - 1).
  4. Simplification: Simplify the formula: an=5+12n−12a_n = 5 + 12n - 12.
  5. Combining Terms: Combine like terms: an=12n−7a_n = 12n - 7.

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