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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=65a_1 = 65\newlinean=an−1+19a_n = a_{n - 1} + 19\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=65a_1 = 65\newlinean=an−1+19a_n = a_{n - 1} + 19\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term: The initial term is a1=65a_1 = 65.
  2. Recursive Formula: The recursive formula is an=an−1+19a_n = a_{n - 1} + 19. This means each term is 1919 more than the previous term.
  3. Explicit Formula: To find the explicit formula, we start with the first term and add 19(n−1)19(n - 1) to it, because the first term does not need to be increased, but every term after that is increased by 1919.
  4. Simplify Formula: So the explicit formula is an=65+19(n−1)a_n = 65 + 19(n - 1).
  5. Combine Like Terms: Simplify the formula: an=65+19n−19a_n = 65 + 19n - 19.
  6. Combine Like Terms: Simplify the formula: an=65+19n−19a_n = 65 + 19n - 19.Combine like terms: an=19n+46a_n = 19n + 46.

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