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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=29a_1 = 29\newlinean=an−1−12a_n = a_{n - 1} - 12\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=29a_1 = 29\newlinean=an−1−12a_n = a_{n - 1} - 12\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term and Recursive Formula: Initial term is a1=29a_1 = 29. Recursive formula is an=an−1−12a_n = a_{n - 1} - 12. This is an arithmetic sequence because each term is found by subtracting a constant from the previous term.
  2. Common Difference: The common difference dd in this arithmetic sequence is −12-12, since each term is 1212 less than the previous term.
  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=29a_1 = 29 and d=−12d = -12.
  4. Substitute Values: Substitute the values into the formula: an=29+(−12)(n−1)a_n = 29 + (-12)(n - 1).
  5. Simplify Formula: Simplify the formula: an=29−12n+12a_n = 29 - 12n + 12.
  6. Combine Like Terms: Combine like terms: an=41−12nan = 41 - 12n.

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