Question

which explicit formula describes the sequence $-9, -3, 3, 9, 15, ...$?
a. $a_n = 6n + 15$
b. $a_n = 6n - 15$
c. $a_n = 9n - 6$
d. $a_n = 9n + 6$

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence with first term $a_1=-9$, common difference $d = -3 - (-9) = 6$.

Step2: Recall arithmetic sequence formula

The explicit formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$.

Step3: Substitute values into formula

Substitute $a_1=-9$ and $d=6$:

$$\begin{align*} a_n &= -9 + (n-1)\times6\\ &= -9 + 6n - 6\\ &= 6n - 15 \end{align*}$$

Step4: Verify with $n=2$

For $n=2$, $a_2=6\times2 -15=12-15=-3$, which matches the sequence.

Answer:

B. $a_n = 6n - 15$