Answer
$a_{43}=-82$
Work Step by Step
Recall:
The $n^{\text{th}}$ term of an arithmetic sequence is given by the formula
$$a_n=a_1+(n-1)d$$
where
$a_1$ = first term
$d$ - common difference
The given arithmetic sequence has:
$a_1=2$
$d=-2$
$a_n=-82$
To find the value of $n$, substitute the given values into the formula above to obtain:
\begin{align*}
a_n&=a_1+(n-1)d\\
-82&=2+(n-1)-2\\
-82-2&=-2(n)-(-2)(1)\\
-84&=-2n+2\\
-84-2&=-2n\\
-86&=-2n
\end{align*}
Divide $-2$ to both sides to obtain:
$$43=n$$
Thus, $-82$ is the $43^{\text{rd}}$ term of the sequence.
