Respuesta :

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For sequence: 17,8,-1, ., the explicit formula is a(n) = 26 - 9n, the recursive formula is a(n) = a(n-1) - 9

To find the recursive and explicit formula, we need to find the common difference (d) first.

In an arithmetic sequence, the common difference is the difference between two consecutive terms.

So, in the given sequence: 17,8,-1, ..

d = a(2) - a(1) = a(3) - a(2)

d = 8 - 17 = -1 - 8 = -9

  • Recursive formula : the formula of nth term in relation with (n-1)th term.
    a(n) = a(n-1) + d
    Substitute d = -9, we get the recursive formula is:
    a(n) = a(n-1) - 9
  • Explicit formula: the formula of nth term in relation with the first term and the common difference.
    a(n) = a(1) + (n-1) . d
    In the given sequence, a(1) = 17, and d = -9, hence:
    a(n) = 17 + (n-1) . (-9)
    a(n) = 17 - 9n + 9
    a(n) = 26 - 9n

Learn more about arithmetic sequences or progression here:

https://brainly.com/question/27902540

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