an = 7n - 189

a_n = 7n-189

−182, −175, −168, −161,...

an = 7 (n − 27)

Answer choice:

an = 7n − 189

What I use for the general form for the n'th term of an arithmetic sequence is:

a(n) = a₁ + b(n - 1)

Where a₁ is the first term (-182 here)

b is the common difference (+7 here)

and n is the "nth" number, so remains a variable. So if we substitute what we have and simplify, we get:

a(n) = -182 + 7(n - 1)

a(n) = -182 + 7n - 7

a(n) = -189 + 7n

or

a(n) = 7n - 189

(answer B)

an=7n−189