Answer
$a_n = -3n + 65$
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 $62$. Let's find the common difference by subtracting one term from the one following it:
$d = 59 - 62 = -3$
The common difference $d$ is $-3$.
Now we can plug these values into the the explicit formula for arithmetic sequences:
$a_n = 62 + (n - 1)(-3)$
Use distributive property:
$a_n = 62 - 3n + 3$
Combine like terms:
$a_n = -3n + 65$
