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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=7a_1 = 7\newlinean=an−1+12a_n = a_{n - 1} + 12\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=7a_1 = 7\newlinean=an−1+12a_n = a_{n - 1} + 12\newlinean=_a_n = \_
  1. Initial Term: 77: The initial term is a1=7a_1 = 7.
  2. Recursive Formula: an=an−1+12a_n = a_{n - 1} + 12: The recursive formula is an=an−1+12a_n = a_{n - 1} + 12. This means each term is 1212 more than the previous term.
  3. Explicit Formula Derivation: To find the explicit formula, we start with the first term and add 1212 times the (n−1)(n-1) to account for the difference between terms.
  4. Explicit Formula: an=12n−5a_n = 12n - 5: So, the explicit formula is an=7+12(n−1)a_n = 7 + 12(n - 1).
  5. Explicit Formula: an=12n−5a_n = 12n - 5: So, the explicit formula is an=7+12(n−1)a_n = 7 + 12(n - 1).Simplify the formula: an=7+12n−12a_n = 7 + 12n - 12.
  6. Explicit Formula: an=12n−5a_n = 12n - 5: So, the explicit formula is an=7+12(n−1)a_n = 7 + 12(n - 1). Simplify the formula: an=7+12n−12a_n = 7 + 12n - 12. Combine like terms: an=12n−5a_n = 12n - 5.

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