Answer:
Part A) common ratio = (-2)
Part B). [tex]a_{0}=\frac{11}{2}[/tex]
[tex]a_{1}=(-44)[/tex]
Step-by-step explanation:
The given geometric sequence is [tex]a_{0}, -11, 22, a_{1}, 88, -176[/tex]
A). We have to find the common ratio of the given sequence
Common ratio = [tex]\frac{22}{(-11)}=(-2)[/tex]
B). In this part we have to find the missing terms
Since explicit formula of geometric sequence is
[tex]T_{n}=a(r)^{n-1}[/tex]
So [tex]T_{2}=a_{0}(r)^{2-1}[/tex]
-11 = [tex]a_{0}(-2)^{2-1}=a_{0}(-2)[/tex]
[tex]a_{0}=\frac{-11}{-2}= \frac{11}{2}[/tex]
Now [tex]a_{1}=(\frac{11}{2})(-2)^{4-1}=\frac{11}{2}(-2)^{3}[/tex]
[tex]a_{1}= \frac{11}{2}(-8)[/tex]
[tex]a_{1}=(11).(-4)=(-44)[/tex]
Answer will be [tex]a_{1}=(-44)[/tex] and [tex]a_{0}=\frac{11}{2}[/tex].
