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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=−57a_1 = -57\newlinean=an−1−16a_n = a_{n - 1} - 16\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=−57a_1 = -57\newlinean=an−1−16a_n = a_{n - 1} - 16\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term and Recursive Formula: Initial term is a1=−57a_1 = -57. Recursive formula is an=an−1−16a_n = a_{n - 1} - 16. This is an arithmetic sequence with a common difference of −16-16.
  2. Explicit Formula Calculation: To find the explicit formula, use the arithmetic sequence formula an=a1+(n−1)da_n = a_1 + (n - 1)d, where dd is the common difference.
  3. Substitution and Simplification: Substitute a1=−57a_1 = -57 and d=−16d = -16 into the formula: an=−57+(n−1)(−16)a_n = -57 + (n - 1)(-16).
  4. Combining Like Terms: Simplify the formula: an=−57−16n+16a_n = -57 - 16n + 16.
  5. Final Simplification: Combine like terms: an=−16n−57+16a_n = -16n - 57 + 16.
  6. Final Simplification: Combine like terms: an=−16n−57+16a_n = -16n - 57 + 16. Final simplification: an=−16n−41a_n = -16n - 41.

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