Question

Write an explicit rule for the sequence 12, 8, 4, 0?

A. an = -4n + 12
B. an = 4n + 12
C. an= -4n + 16
D. an= 4n + 16

Answer 1

The correct explicit rule for the sequence 12, 8, 4, 0 is represented by the formula an = -4n + 16, where 'n' is the term number in the sequence.

Step-by-step explanation:

To write an explicit rule for the sequence 12, 8, 4, 0, we first observe the pattern: each term decreases by 4 from the previous term. Taking the initial term (12) as a starting point, we can express the n-th term (an) as the initial term minus 4 times (n-1), because for the first term, when n = 1, (n-1) = 0 and the sequence should start at 12.

Therefore, the rule can be written as an = 12 - 4(n-1). Simplifying this expression, we get an = 12 - 4n + 4 which further simplifies to an = -4n + 16.

Hence, the correct answer is C. an = -4n + 16.