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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=4a_1 = 4\newlinean=an−1+17a_n = a_{n - 1} + 17\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=4a_1 = 4\newlinean=an−1+17a_n = a_{n - 1} + 17\newlinean=_a_n = \_
  1. Initial Term: The initial term is a1=4a_1 = 4.
  2. Recursive Formula: The recursive formula is an=an−1+17a_n = a_{n - 1} + 17. This means each term is 1717 more than the previous term.
  3. Find Explicit Formula: To find the explicit formula, we start with the initial term and add 1717 for each subsequent term. So for the second term, a2=a1+17=4+17a_2 = a_1 + 17 = 4 + 17.
  4. Calculate Second Term: For the third term, a3=a2+17=(4+17)+17a_3 = a_2 + 17 = (4 + 17) + 17.
  5. Calculate Third Term: We notice that each term is the initial term plus 1717 times the position minus 11. So, an=4+17(n−1)a_n = 4 + 17(n - 1).
  6. General Formula: Simplify the formula: an=4+17n−17a_n = 4 + 17n - 17.
  7. Simplify Formula: Combine like terms: an=17n−13a_n = 17n - 13.

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