Answer:
20 - 2n
Step-by-step explanation:
The sequence is arithmetic since the difference between consecutive terms is constant, that is
d = 16 - 18 = 14 - 16 = 12 - 14 = - 2
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 18 and d = - 2, thus
[tex]a_{n}[/tex] = 18 - 2(n - 1) = 18 - 2n + 2 = 20 - 2n
[tex]a_{n}[/tex] = 20 - 2n
If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].
This sequence is an example of an arithmetic sequence, since each consecutive pair of elements has one and only one difference, that is to say:
[tex]r = x_{i+1}-x_{i}[/tex], [tex]\forall\,i\in \mathbb{N}[/tex] (1)
The expression for any arithmetic sequence is described by the following formula:
[tex]f(n) = x_{1} + r\cdot (n-1)[/tex], [tex]n \ge 1[/tex] (2)
Where:
If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].
We kindly invite to check this question on number sequences: https://brainly.com/question/7043242
