Answer:
You can check the answer by yourself after seeing the below answer.
Step-by-step explanation:
A sequence is geometric only if has common ratio i.e. [tex]r=\frac{a2}{a1} =\frac{a3}{a2}[/tex] whiere a1,a2 and a3 are first,second and third term of the sequence respectively.
1) Common ratio [tex]r=\frac{-18}{-3}=\frac{-108}{-18}=6\\[/tex]
Explicit formula [tex]a_{n} =a_{1} .r^{n-1}[/tex]
Now using the above formula, we can find [tex]8^{th} term=-3*(6)^{8-1} =-3*6^{7}=-839808.[/tex]
2) Here
[tex]\frac{a2}{a1}\neq \frac{a3}{a2}\\\frac{-2}{-4}\neq \frac{1}{-2}\\\frac{1}{2}\neq\frac{1}{-2}[/tex] so this is not geometric sequence so no need to proceed further.
3) Common ratio [tex]r=\frac{15}{-3}=\frac{-75}{15}=-5\\[/tex]
Explicit formula [tex]a_{n} =a_{1} .(-5)^{n-1}[/tex]
Now using the above formula, we can find [tex]8^{th} term=-3*(-5)^{8-1} =-3*(-5)^{7}=234375.[/tex]
4) Common ratio [tex]r=\frac{-6}{1}=\frac{36}{-6}=-6\\[/tex]
Explicit formula [tex]a_{n} =a_{1} .(-6)^{n-1}[/tex]
Now using the above formula, we can find [tex]8^{th} term=1*(-6)^{8-1} =1*(-6)^{7}=-279936.[/tex]
5)Common ratio [tex]r=\frac{-8}{4}=\frac{16}{-8}=-2\\[/tex]
Explicit formula [tex]a_{n} =a_{1} .(-2)^{n-1}[/tex]
Now using the above formula, we can find [tex]8^{th} term=4*(-2)^{8-1} =4*(-2)^{7}=-512.[/tex]
6)Common ratio [tex]r=\frac{-8}{-2}=\frac{-32}{-8}=4\\[/tex]
Explicit formula [tex]a_{n} =a_{1} .(4)^{n-1}[/tex]
Now using the above formula, we can find [tex]8^{th} term=-2*(4)^{8-1} =-2*(4)^{7}=-32768.[/tex]
