Answer:
[tex]a_n = 7n - 189[/tex]
Step-by-step explanation:
The given sequence is -182, -175, -168, -161, ...
It is an arithmetic sequence, because the difference between the successive term is the same constant.
d = -175 - (-182) = -175 +182 = 7
d = -168 - (-175) = -168 + 175 = 7
So the difference (d) = 7
The first term is [tex]a_1 = -182[/tex]
The explicit formula of an arithmetic sequence is [tex]a_n = a_1 + (n -1)d[/tex]
Now plug in a_1 = -182 and d = 7
[tex]a_n = -182 + (n-1)7[/tex]
[tex]a_n = -182 + 7n - 7[/tex]
Simplify the like terms
[tex]a_n = 7n - 189[/tex]
