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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=55a_1 = 55\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=55a_1 = 55\newlinean=an−1+13a_n = a_{n - 1} + 13\newlinean=_a_n = \_
  1. Initial Term: The initial term is a1=55a_1 = 55.
  2. Recursive Formula: The recursive formula is an=an−1+13a_n = a_{n - 1} + 13.
  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: The sequence is arithmetic because each term increases by a constant difference, which is 1313.
  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=55a_1 = 55 and d=13d = 13 into the formula: an=55+(n−1)×13a_n = 55 + (n - 1) \times 13.
  7. Simplify Formula: Simplify the formula: an=55+13n−13a_n = 55 + 13n - 13.
  8. Combine Like Terms: Combine like terms: an=13n+42an = 13n + 42.

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