Answer:
The function [tex]a_n=2n-3[/tex] describes the arithmetic sequence.
Step-by-step explanation:
Given the sequence
-1, 1, 3, 5, 7, 9, 11, 13
An arithmetic sequence has a constant difference 'd' is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
Compute the differences between all the adjacent terms:
[tex]1-\left(-1\right)=2,\:\quad \:3-1=2,\:\quad \:5-3=2,\:\quad \:7-5=2,\:\quad \:9-7=2,\:\quad \:11-9=2,\:\quad \:13-11=2[/tex]
As the difference between all of the adjacent terms is the same and equal to
[tex]d=2[/tex]
As the first element is
[tex]a_1=-1[/tex]
so the term will be:
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=2\left(n-1\right)-1[/tex]
[tex]a_n=2n-3[/tex]
So, the function [tex]a_n=2n-3[/tex] describes the arithmetic sequence.
