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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=31a_1 = 31\newlinean=an−1+13a_n = a_{n - 1} + 13\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=31a_1 = 31\newlinean=an−1+13a_n = a_{n - 1} + 13\newlinean=_a_n = \_
  1. Identify Sequence Type: First term is a1=31a_1 = 31, and the recursive formula is an=an−1+13a_n = a_{n - 1} + 13, which means it's an arithmetic sequence cuz each term is just the previous one plus 1313.
  2. Calculate Common Difference: The common difference dd is the amount we're adding each time, so d=13d = 13.
  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 just gotta plug in the numbers we know.
  4. Substitute Values: So, an=31+13(n−1)a_n = 31 + 13(n - 1). Now we do the math.
  5. Simplify Expression: an=31+13n−13a_n = 31 + 13n - 13. Combine like terms.
  6. Final Explicit Formula: an=13n+18a_n = 13n + 18. That's the explicit formula, done!

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