Answer:
Option C [tex]a_n=-17+5(n-1)[/tex]
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference
The formula of the nth term of the arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex]
where
[tex]a_n[/tex] is the nth term
[tex]a_1[/tex] is the first term
d is the common difference
n is the number of terms
In this problem we have
[tex]a_1=-17[/tex]
[tex]a_2=-12[/tex]
[tex]a_3=-7[/tex]
[tex]a_4=-2[/tex]
Find the common difference d
[tex]a_2-a_1=-12-(-17)=5[/tex]
[tex]a_3-a_2=-7-(-12)=5[/tex]
[tex]a_4-a_3=-2-(-7)=5[/tex]
The common difference is d=5
substitute the values in the formula
[tex]a_n=-17+5(n-1)[/tex]
