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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=−14a_1 = -14\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=−14a_1 = -14\newlinean=an−1+15a_n = a_{n - 1} + 15\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term: Initial term is a1=−14a_1 = -14. Recursive formula is an=an−1+15a_n = a_{n - 1} + 15. This is an arithmetic sequence because each term increases by a constant amount.
  2. Common Difference: The common difference dd in the arithmetic sequence is 1515 because an=an−1+15a_n = a_{n - 1} + 15.
  3. 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=−14a_1 = -14 and d=15d = 15.
  4. Substitute Values: Substitute the values into the formula: an=−14+15(n−1)a_n = -14 + 15(n - 1).
  5. Simplify Formula: Simplify the formula: an=−14+15n−15a_n = -14 + 15n - 15.
  6. Combine Like Terms: Combine like terms: an=15n−29an = 15n - 29.

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