## Algebra 2 Common Core

$a_{43}=-82$
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.