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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=50a_1 = 50\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=50a_1 = 50\newlinean=an−1+1a_n = a_{n - 1} + 1\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term: The initial term is a1=50a_1 = 50.
  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 start with the initial term and add the common difference (which is 11) multiplied by (n−1)(n - 1), because the sequence starts at n=1n = 1.
  4. Simplify Formula: So, the explicit formula is an=50+(n−1)×1a_n = 50 + (n - 1) \times 1.
  5. Combine Like Terms: Simplify the formula: an=50+n−1a_n = 50 + n - 1.
  6. Combine Like Terms: Simplify the formula: an=50+n−1a_n = 50 + n - 1. Combine like terms: an=n+49a_n = n + 49.

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