Write an equation for the $n$ th term of the arithmetic seqeuence. Then find $a_{10}$ . $-6,-9,-12,-15,\ ...$ $a_n=$ $a_{10}=$

Answer 1

From the sequence, we see that when $a_1 = -6$, $a_2 = -9$, $a_3 = -12$, $\ldots$. We see that as $n$ increases by 1, the sequence $a_n$ increases by -3. We can create a map, say $f:\mathbb{Z}\to\mathbb{Z}$ defined by the equation $f(n) = -3(n+1)$. By this definition, $f(10) = -3(10+1) = -3(11) = -33$. Replace $f(n)$ by $a_n$. Thus, $\boxed{a_n = -3(n+1)}$ and $\boxed{a_{10} = -33}$.