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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=3a_1 = 3\newlinean=an−1−7a_n = a_{n - 1} - 7\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=3a_1 = 3\newlinean=an−1−7a_n = a_{n - 1} - 7\newlinean=_a_n = \_
  1. Identify Sequence Type: First term is a1=3a_1 = 3, and the recursive formula is an=an−1−7a_n = a_{n-1} - 7. This looks like an arithmetic sequence cuz the difference is constant.
  2. Calculate Common Difference: The common difference dd is −7-7 since each term is 77 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). We plug in a1=3a_1 = 3 and d=−7d = -7.
  4. Simplify Expression: So, an=3+(−7)(n−1)a_n = 3 + (-7)(n - 1). Let's simplify that.
  5. Combine Like Terms: an=3−7n+7an = 3 - 7n + 7. Combine like terms, 3+73 + 7 is 1010.

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