Question

Which explicit formula describes the sequence −9, −3, 3, 9, 15, …?

A. an = 9n + 6
B. an = 6n + 15
C. an = 6n - 15
D. an = 9n – 6

Answer 1

The explicit formula for the sequence -9, -3, 3, 9, 15, ... is given by an = 6n - 15.

Step-by-step explanation:

The sequence -9, -3, 3, 9, 15, ... is an arithmetic sequence with a common difference of 6. To find the explicit formula for the sequence, we can start with the first term and add the product of the common difference and the position of the term (n-1).

The explicit formula for an arithmetic sequence is an = a1 + (n-1)d, where an is the nth term of the sequence, a1 is the first term, and d is the common difference.

In this case, the first term is -9 and the common difference is 6, so the explicit formula for the sequence is an = -9 + 6(n-1), which simplifies to an = -9 + 6n - 6 or an = 6n - 15.