Find the indicated term of the arithmetic sequence based on the given information.
-$a _ { 1 } = 13$ and $a _ { 18 } = - 55 ;$ Find $a _ { 9 }$
A) $- 91$
B) $- 19$
C) $- 55$
D) $- 23$

Question

Quizplus · Accepted Answer

The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. Given $a_1 = 13$ and $a_{18} = -55$, we can find $d$ by rearranging the formula: $-55 = 13 + (18 - 1)d$, which simplifies to $-55 = 13 + 17d$, leading to $-68 = 17d$, so $d = -4$. To find $a_9$, we use $a_9 = 13 + (9 - 1)(-4) = 13 - 32 = -19$.

Find the Indicated Term of the Arithmetic Sequence Based on the Given