Question

Find the 30th term in the sequence: 18,15,12

Answer 1

Since it is going down a constant rate (-3) keep subtracting 3 until you get to the 30th term.

Answer 2

Hmmm 18, 15, 12?   what's going on?  wait a second, 15 is 18-3, and 12 is 15 -3, so... to get the next number is really just subtracting 3 from the current one, meaning, is an arithmetic sequence, the first term's value is 18, and the common difference is -3.

now, what is the 30th term anyway?

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ a_1=18\\ d=-3\\ n=30 \end{cases} \\\\\\ a_n=18+(30-1)(-3)\implies a_{30}=18+(30-1)(-3) \\\\\\ a_{30}=18-87\implies \boxed{a_{30}=-69}$