Answer:
D.) Is the correct answer.
Step-by-step explanation:
The equation for geometric sequence is:
[tex]a_n=a_1 r^{n-1}[/tex]
Since we know [tex]a_1=-3[/tex] and [tex]a_n=a_{n-1}(\frac{1}{8})[/tex]
Let's calculate the first three terms using the top equations, but since we already know what [tex]a_1[/tex] is then we only need [tex]a_2[/tex] and [tex]a_3[/tex].
Calculate [tex]a_2[/tex] let n=2 and so:
[tex]a_2=a_{2-1}(\frac{1}{8})\\\\a_2=a_1(\frac{1}{8})=-3 (\frac{1}{8})= -\frac{3}{8}[/tex]
Calculate [tex]a_3[/tex] let n=3 and so:
[tex]a_3=a_{3-1}(\frac{1}{8})=a_2(\frac{1}{8})=-\frac{3}{8}(\frac{1}{8})=-\frac{3}{64}[/tex]
Now the only answer choice that will return the same values is:
D.) [tex]a_n=-3(\frac{1}{8})^{n-1}[/tex]
Check:
Let n=1:
[tex]a_1=-3(\frac{1}{8})^{1-1}=-3(\frac{1}{8})^0=-3(1)=-3\\[/tex]
Let n=2:
[tex]a_2=-3(\frac{1}{8})^{2-1}=-3(\frac{1}{8})^1=-\frac{3}{8}[/tex]
Finally let n=3 to check our answers:
[tex]a_3=-3(\frac{1}{8})^{3-1}=-3(\frac{1}{8})^2=-3(\frac{1}{64})=-\frac{3}{64}[/tex]
Mark brainliest, much appreciated.
