Answer:
[tex]\large\boxed{A)\ 5.5\ and\ -44}[/tex]
[tex]\large\boxed{B)\ a_1=5.5,\ a_{n+1}=-2a_n}[/tex]
Step-by-step explanation:
A)
If a, b and c are a geometric sequence, then ac = b².
We have:
x, -11, 22, y, 88, -176
Therefore
[tex]22x=(-11)^2[/tex]
[tex]22x=121[/tex] divide both sides by 22
[tex]x=5.5[/tex]
and
[tex]-176y=88^2[/tex]
[tex]-176y=7744[/tex] divide both sides by (-176)
[tex]y=-44[/tex]
B)
Find the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}[/tex]
[tex]r=\dfrac{-11}{5.5}=-2[/tex]
[tex]a_1=5.5\\\\a_{n+1}=-2a_n[/tex]
