Question

A geometric sequence is shown below: a0, -11, 22, a1, 88, -176. A) What is the common ratio for this geometric sequence? a2 B) What are the missing terms in the geometric sequence shown above?

Answer 1

176/88=2
22/11=2
Numbers are alternating in negativity, so ratio is (-2)
-11/-2=a0=5.5
88/-2=a1=-44

Answer 2

Part A) common ratio = (-2)

Part B).
`a_(0)=(11)/(2)`

`a_(1)=(-44)`

Explanation:

The given geometric sequence is
`a_(0), -11, 22, a_(1), 88, -176`

A). We have to find the common ratio of the given sequence

Common ratio =
`(22)/((-11))=(-2)`

B). In this part we have to find the missing terms

Since explicit formula of geometric sequence is

`T_(n)=a(r)^(n-1)`

So
`T_(2)=a_(0)(r)^(2-1)`

-11 =
`a_(0)(-2)^(2-1)=a_(0)(-2)`

`a_(0)=(-11)/(-2)= (11)/(2)`

Now
`a_(1)=((11)/(2))(-2)^(4-1)=(11)/(2)(-2)^(3)`

`a_(1)= (11)/(2)(-8)`

`a_(1)=(11).(-4)=(-44)`

Answer will be
`a_(1)=(-44)` and
`a_(0)=(11)/(2)`.