Question

A sequence is defined by f(0)=-4, f(n)=f(n-1)-2 for n>1. write a definition for the nth term.

Answer 1

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

$a_n = -2 - 2n, n \geq 1$

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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:

$a_n = a_1 + (n-1)d$

• In which $a_1$ is the first term.

In the recursive sequence, we have that:

$f(0) = -4$

$f(n) = f(n-1) - 2$

Then

$f(1) = f(0) - 2 = -4 - 2 = -6$

$f(2) = f(1) - 2 = -6 - 2 = -8$

And so on...

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

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

$a_n = a_1 + (n-1)d$

$a_n = -4 - 2(n-1)$

$a_n = -4 - 2n + 2$

$a_n = -2 - 2n, n \geq 1$

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