Answer:
The 8th term of geometric sequence is -8748
ie., [tex]a_{8}=-8748[/tex]
Step-by-step explanation:
Given geometric sequence is 4,-12,36,...
Geometric sequence can be written as
[tex]a_{1},a_{2},a_{3},..,[/tex]
[tex]a_{1}=4=a[/tex]
[tex]a_{2}=-12=ar[/tex]
[tex]a_{3}=36=ar^2[/tex]
and so on.
common ratio is [tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]r=\frac{-12}{4}[/tex]
[tex]r=-3[/tex]
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]r=\frac{36}{-12}[/tex]
[tex]r=-3[/tex]
Therefore [tex]r=-3[/tex]
Geometric sequence of nth term is [tex]a_{n}=ar^{n-1}[/tex]
To find the 8th term:
[tex]a_{8}=ar^{8-1}[/tex]
[tex]a_{8}=ar^{7}[/tex]
here a=4 and r=-3
[tex]a_{8}=ar^{7}[/tex]
[tex]=4\times (-3)^7[/tex]
[tex]=4\times (-2187) [/tex]
[tex]=-8748[/tex]
[tex]a_{8}=-8748[/tex]
Therefore the 8th term of geometric sequence is -8748
