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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=−21a_1 = -21\newlinean=an−1−17a_n = a_{n - 1} - 17\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=−21a_1 = -21\newlinean=an−1−17a_n = a_{n - 1} - 17\newlinean=_a_n = \_
  1. Identify Initial Term: Initial term is a1=−21a_1 = -21. Recursive formula is an=an−1−17a_n = a_{n - 1} - 17. This looks like an arithmetic sequence with a common difference of −17-17.
  2. Find Recursive Formula: To find the explicit formula for an arithmetic sequence, we use an=a1+d(n−1)a_n = a_1 + d(n - 1), where dd is the common difference.
  3. Calculate Explicit Formula: Substitute a1=−21a_1 = -21 and d=−17d = -17 into the formula. So, an=−21+(−17)(n−1)a_n = -21 + (-17)(n - 1).
  4. Substitute Values: Now, simplify the formula. an=−21−17n+17a_n = -21 - 17n + 17.
  5. Simplify Formula: Combine like terms. an=−17n−21+17a_n = -17n - 21 + 17.
  6. Combine Like Terms: Finish simplifying. an=−17n−4an = -17n - 4.

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