Question

a sequence is shown below.
-20, -17, -14, -11, -8, ...
which explicit equation can be used to determine the value of the nth term in the sequence?
$a_n = n - 23$
$a_n = 3n + 23$
$a_n = 3n - 23$
$a_n = n + 3$

Explanation:

Step1: Identify sequence type & parameters

This is an arithmetic sequence. The first term $a_1 = -20$, common difference $d = -17 - (-20) = 3$.

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

$$\begin{align*} a_n &= -20 + (n-1) \times 3 \\ &= -20 + 3n - 3 \\ &= 3n - 23 \end{align*}$$

Answer:

$a_n = 3n - 23$