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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=18a_1 = 18\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=18a_1 = 18\newlinean=an−1+1a_n = a_{n - 1} + 1\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term: The initial term is a1=18a_1 = 18.
  2. Recursive Formula: The recursive formula is an=an−1+1a_n = a_{n - 1} + 1, which means each term is 11 more than the previous term.
  3. Explicit Formula: To find the explicit formula, we need to express ana_n in terms of nn using the initial term and the common difference.
  4. Sequence Type: Since the common difference is 11, the sequence is arithmetic.
  5. Arithmetic Sequence Formula: The explicit formula for an arithmetic sequence is an=a1+(n−1)da_n = a_1 + (n - 1)d, where dd is the common difference.
  6. Substitute Values: Substitute a1=18a_1 = 18 and d=1d = 1 into the formula: an=18+(n−1)(1)a_n = 18 + (n - 1)(1).
  7. Simplify Formula: Simplify the formula: an=18+n−1a_n = 18 + n - 1.
  8. Combine Like Terms: Combine like terms: an=n+17an = n + 17.

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