Question

How many terms are in the arithmetic sequence 9, 2, −5, . . . , −187?

Answer 1

9, 2, -5... so is going down by 7 each time, meaning the "common difference" is -7.

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ a_1=9\\ d=-7\\ a_n=-187 \end{cases} \\\\\\ -187=9+(n-1)(-7)\implies -187=9-7n+7 \\\\\\ 7n=9+7+187\implies 7n=203\implies n=\cfrac{203}{7}\implies \boxed{n=29}$