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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+11a_n = a_{n - 1} + 11\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+11a_n = a_{n - 1} + 11\newlinean=_____a_n = \_\_\_\_\_
  1. Identify Sequence Type: Initial term is a1=−19a_1 = -19, and the recursive formula is an=an−1+11a_n = a_{n - 1} + 11. This looks like an arithmetic sequence because each term is the previous term plus a constant.
  2. Find Common Difference: The common difference dd in the recursive formula an=an−1+11a_n = a_{n - 1} + 11 is 1111 because that's what we're adding each time to get the next term.
  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 know a1=−19a_1 = -19 and d=11d = 11.
  4. Substitute Values: Plug the values into the formula: an=−19+11(n−1)a_n = -19 + 11(n - 1).
  5. Simplify Formula: Simplify the formula: an=−19+11n−11a_n = -19 + 11n - 11.
  6. Combine Terms: Combine like terms: an=11n−30a_n = 11n - 30.

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