Question

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.

A. a_n = 9 − 3(n − 1) where n ≤ 9
B. a_n = 9 − 3(n − 1) where n ≥ 1
C. a_n = 9 − 6(n − 1) where n ≤ 9
D. a_n = 9 − 6(n − 1) where n ≥ 1

Answer 1

D) a_n = 9 − 6(n − 1) where n ≥ 1

Answer 2

Using the formula:
an = a1 +(n-1)d
a1 = 9 (first term of the sequence)
d= -6 (common difference)

Substituting into the formula:
an= a1 +(n-1)d
an = 9 + (n-1)(-6)
an = 9 - 6(n-1)

So the best answer is :D. a_n = 9 − 6(n − 1) where n ≥ 1