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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=−9a_1 = -9\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=−9a_1 = -9\newlinean=an−1+11a_n = a_{n - 1} + 11\newlinean=_____a_n = \_\_\_\_\_
  1. Identify Arithmetic Sequence: We got a1=−9a_1 = -9 and an=an−1+11a_n = a_{n-1} + 11, it's an arithmetic sequence cuz each term is just the previous one plus a constant.
  2. Find Common Difference: The common difference dd is the number we add each time, so d=11d = 11.
  3. Apply Explicit Formula: The explicit formula for an arithmetic sequence is an=a1+d(n−1)a_n = a_1 + d(n - 1). Let's plug in what we know: a1=−9a_1 = -9 and d=11d = 11.
  4. Plug in Values: So, an=−9+11(n−1)a_n = -9 + 11(n - 1). Now we just gotta simplify this.
  5. Simplify Expression: an=−9+11n−11a_n = -9 + 11n - 11. Combine like terms, −9-9 and −11-11.
  6. Final Explicit Formula: an=11n−20a_n = 11n - 20. That's it, we got the explicit formula.

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