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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=28a_1 = 28\newlinean=an−1−1a_n = a_{n - 1} - 1\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=28a_1 = 28\newlinean=an−1−1a_n = a_{n - 1} - 1\newlinean=_a_n = \_
  1. Initial Term and Recursive Formula: The initial term is a1=28a_1 = 28. The recursive formula is an=an−1−1a_n = a_{n - 1} - 1, which means each term is 11 less than the previous term.
  2. Expressing in Terms of nn: To find the explicit formula, we need to express ana_n in terms of nn. Since the sequence decreases by 11 each time, we can write an=a1−(n−1)a_n = a_1 - (n - 1).
  3. Substitute and Simplify: Substitute the value of a1a_1 into the formula: an=28−(n−1)a_n = 28 - (n - 1).
  4. Combine Like Terms: Simplify the formula: an=28−n+1a_n = 28 - n + 1.
  5. Combine Like Terms: Simplify the formula: an=28−n+1a_n = 28 - n + 1.Combine like terms: an=29−na_n = 29 - n.

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