Write the first five terms of the geometric sequence. $$a _ { 1 } = 4 , r = - \frac { 1 } { 5 }$$
A) $4 , - 1 , - 6 , - 11 , - 16$
B) $4 , - 20,100 , - 500,2500$
C) $- \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 } , \frac { 4 } { 625 } , - \frac { 4 } { 3125 }$
D) $1,4 , - \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 }$
E) $4 , - \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 } , \frac { 4 } { 625 }$

Question

Quizplus · Accepted Answer

The formula for the $n$th term of the geometric sequence is $a_n=a_1 r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio. Using this formula, we can find the first five terms of the sequence as follows:

\begin{align*}
a_1 &= 4 \
a_2 &= 4\cdot \left(-\frac{1}{5}ight) = -\frac{4}{5} \
a_3 &= 4\cdot \left(-\frac{1}{5}ight)^2 = \frac{4}{25} \
a_4 &= 4\cdot \left(-\frac{1}{5}ight)^3 = -\frac{4}{125} \
a_5 &= 4\cdot \left(-\frac{1}{5}ight)^4 = \frac{4}{625} \
\end{align*}

Therefore, the first five terms of the geometric sequence are $4, -\frac{4}{5}, \frac{4}{25}, -\frac{4}{125}, \frac{4}{625}$, which corresponds to choice $\boxed{	extbf{(E)}}$.

Write the First Five Terms of the Geometric Sequence a1=4,r=−15a _ { 1 } = 4 , r = - \frac { 1 } { 5 }a1​=4,r=−51​

Write the First Five Terms of the Geometric Sequence $a _ { 1 } = 4 , r = - \frac { 1 } { 5 }$