Question

write an explicit formula for the nth term of the following arithmetic sequence. {-5, -3, -1, 1, …} select one: a. $a_n = -2n - 7$ b. $a_n = 2n - 6$ c. $a_n = 2n - 3$ d. $a_n = 2n - 7$

Explanation:

Step1: Recall arithmetic sequence formula

The explicit formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, and $d$ is the common difference.

Step2: Identify $a_1$ and $d$

From the sequence $\{-5, -3, -1, 1, ...\}$, $a_1 = -5$. Calculate $d$: $d = -3 - (-5) = 2$.

Step3: Substitute into the formula

$$\begin{align*} a_n &= -5 + (n-1) \times 2 \\ &= -5 + 2n - 2 \\ &= 2n - 7 \end{align*}$$

Step4: Match with options

The derived formula matches option D.

Answer:

D. $a_n = 2n - 7$