Answer
$a_n = 9n - 11$
Work Step by Step
Use the explicit formula for arithmetic sequences, which is $a_n = a + (n - 1)d$, where $a$ is the first term of the sequence and $d$ is the common difference; in this exercise, $a$ is $-2$. Let's find the common difference by subtracting one term from the one following it:
$d = 7 - (-2) = 9$
The common difference $d$ is $9$.
Now we can plug these values into the the explicit formula for arithmetic sequences:
$a_n = -2 + (n - 1)9$
Use distributive property:
$a_n = -2 + 9n - 9$
Combine like terms:
$a_n = 9n - 11$
