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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=4a_1 = 4\newlinean=an−1−15a_n = a_{n - 1} - 15\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=4a_1 = 4\newlinean=an−1−15a_n = a_{n - 1} - 15\newlinean=_a_n = \_
  1. Identify Arithmetic Sequence: We got a1=4a_1 = 4 and an=an−1−15a_n = a_{n-1} - 15. This looks like an arithmetic sequence cuz the difference between terms is constant.
  2. Find Common Difference: The common difference dd is −15-15 since each term is 1515 less than the one before it.
  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=4a_1 = 4 and d=−15d = -15.
  4. Plug in Values: So, an=4+(−15)(n−1)a_n = 4 + (-15)(n - 1). Now we just gotta simplify this.
  5. Simplify Expression: an=4−15n+15a_n = 4 - 15n + 15. Combine like terms and we get an=−15n+19a_n = -15n + 19.

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