Write the first five terms of the geometric sequence, given $a_{1}=-9$ and $r=-\frac{1}{3}$ .
A) $-9,3,-1, \frac{1}{3},-\frac{1}{9}$
B) $-9,-3,1,-\frac{1}{3},-\frac{1}{9}$
C) $-9,27,-1, \frac{1}{9},-\frac{1}{27}$
D) $-27,9,1, \frac{1}{9},-\frac{1}{27}$
E) $- 27,9 , - 1 , - \frac { 1 } { 3 } , - \frac { 1 } { 27 }$

Question

Quizplus · Accepted Answer

The formula for the $n$th term of a geometric sequence is $a_{n}=a_{1}r^{n-1}$. Plugging in $a_{1}=-9$ and $r=-\frac{1}{3}$, we get $a_{n}=-9\cdot\left(-\frac{1}{3}ight)^{n-1}$. Thus, the first five terms are:

\begin{align*}
a_{1}&=-9\
a_{2}&=-9\cdot\left(-\frac{1}{3}ight)^{1}=\boxed{3}\
a_{3}&=-9\cdot\left(-\frac{1}{3}ight)^{2}=\boxed{-1}\
a_{4}&=-9\cdot\left(-\frac{1}{3}ight)^{3}=\boxed{\frac{1}{3}}\
a_{5}&=-9\cdot\left(-\frac{1}{3}ight)^{4}=\boxed{-\frac{1}{9}}
\end{align*}

Therefore, the answer is $\boxed{	extbf{(A)}}.$

Write the First Five Terms of the Geometric Sequence, Given a1=−9a_{1}=-9a1​=−9

Write the First Five Terms of the Geometric Sequence, Given $a_{1}=-9$