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Which word best describes this formula for the sequence ana_n?\newlinean=−4an−1+an−4−12n2−13n+14a_n = -4a_{n - 1} + a_{n - 4} - 12n^2 - 13n + 14\newlineChoices:\newline(A)explicit\newline(B)recursive\newline

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Q. Which word best describes this formula for the sequence ana_n?\newlinean=−4an−1+an−4−12n2−13n+14a_n = -4a_{n - 1} + a_{n - 4} - 12n^2 - 13n + 14\newlineChoices:\newline(A)explicit\newline(B)recursive\newline
  1. Identify Formula Type: The formula given is an=−4an−1+an−4−12n2−13n+14a_n = -4a_{n - 1} + a_{n - 4} - 12n^2 - 13n + 14. We need to determine if it's explicit or recursive.
  2. Explicit vs Recursive: An explicit formula provides a way to find the nnth term without knowing any other terms in the sequence. A recursive formula provides a way to find the nnth term using one or more previous terms.
  3. Dependence on Previous Terms: The formula has terms like an−1a_n - 1 and an−4a_n - 4, which are previous terms in the sequence. This means the current term ana_n is defined using previous terms.
  4. Conclusion: Since the formula depends on previous terms, it is a recursive formula.

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