Question

Which type of sequence is represented by the table below?

x 1 2 3 4
y 5 3 1.8 1.08

The table represents an arithmetic sequence because the successive y-values have a common difference of 6.

The table represents a geometric sequence because the successive y-values have a common ratio of 0.6.

The table represents an arithmetic sequence because the successive y-values have a common difference of 2.

The table represents a geometric sequence because the successive y-values have a common ratio of 1.7.

Answer 1

The table represents a geometric sequence because the successive y-values have a common ratio of 0.6.

Explanation:

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Answer 2

The table represents a geometric sequence because the successive y-values have a common ratio of 0.6.

Explanation:

We are given the values of y as
`a_(1)=5,a_(2)=3,a_(3)=1.8,a_(4)=1.08` where the subscript {1,2,3,4} represents the value of x i.e.
`a_(i)'s` represent the value of y at x=i.

now the following sequence is clearly a geometric sequence as we get a common ratio for the terms :
`(a_(2) )/(a_(1) )=(a_(3) )/(a_(2) )=(a_(4) )/(a_(3) )`

so the common ration here is
`(3)/(5)=(1.8)/(3)=(1.08)/(1.8)=0.6`

Hence the following sequence is a geometric sequence with a common ratio 0.6.