Respuesta :

Using an arithmetic sequence, the formula for the nth term is given by:

[tex]a_n = -2 - 2n, n \geq 1[/tex]

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  • In an arithmetic sequence, the difference between consecutive terms is always the same, and it is called common difference d.
  • The nth term is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

  • In which [tex]a_1[/tex] is the first term.

In the recursive sequence, we have that:

[tex]f(0) = -4[/tex]

[tex]f(n) = f(n-1) - 2[/tex]

Then

[tex]f(1) = f(0) - 2 = -4 - 2 = -6[/tex]

[tex]f(2) = f(1) - 2 = -6 - 2 = -8[/tex]

And so on...

The sequence is: {-4, -6, -8,...}

Which is an arithmetic sequence with [tex]a_1 = -4[/tex] and [tex]d = -2[/tex], thus, the definition for the nth term is:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]a_n = -4 - 2(n-1)[/tex]

[tex]a_n = -4 - 2n + 2[/tex]

[tex]a_n = -2 - 2n, n \geq 1[/tex]

A similar problem is given at https://brainly.com/question/23901992