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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=−25a_1 = -25\newlinean=an−1+16a_n = a_{n - 1} + 16\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=−25a_1 = -25\newlinean=an−1+16a_n = a_{n - 1} + 16\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term: The initial term is a1=−25a_1 = -25.
  2. Recursive Formula: The recursive formula is an=an−1+16a_n = a_{n - 1} + 16. This means each term is 1616 more than the previous term.
  3. Explicit Formula: To find the explicit formula, we start with the first term and add 16(n−1)16(n-1) to it, because the first term does not have the 1616 added to it yet, and each subsequent term adds 1616 once more than the previous term.
  4. Substitute a1a_1: So the explicit formula is an=a1+16(n−1)a_n = a_1 + 16(n-1).
  5. Distribute the 1616: Substitute a1=−25a_1 = -25 into the formula: an=−25+16(n−1)a_n = -25 + 16(n-1).
  6. Combine Like Terms: Distribute the 1616: an=−25+16n−16an = -25 + 16n - 16.
  7. Combine Like Terms: Distribute the 1616: an=−25+16n−16a_n = -25 + 16n - 16.Combine like terms: an=16n−41a_n = 16n - 41.

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