Question

Isaac keeps track of the miles per gallon his car gets per week. He has accumulated the following data:

(1, 24), (2, 24.48), (3, 24.97), (4, 25.47)

What is the common difference or ratio?

The common difference is 0.48.

The common difference is 0.50.

The common ratio is 0.98.

The common ratio is 1.02.

Answer 1

The common ratio is 1.02

Explanation:

An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.

From data the differences between two consecutive terms are:

24.48 - 24 = 0.48

24.97 - 24.48 = 0.49

25.47 - 24.97 = 0.5

Then, there is no common difference and the sequence is not arithmetic.

From data the ratio between two consecutive terms terms are:

24.48/24 = 1.02

24.97/24.48 = 1.02

25.47/24.97 = 1.02

Then, the common ratio is 1.02 and the sequence is a geometric one.

Answer 2

we know that

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant

so

Let

`a1=24 \ a2=24.48\ a3=24.97\ a4=25.47`

`(a2)/(a1) = (24.48)/(24)= 1.02`

`a2=a1*1.02`

`(a3)/(a2) = (24.97)/(24.48)= 1.02`

`a3=a2*1.02`

`(a4)/(a3) = (25.47)/(24.97)= 1.02`

`a4=a3*1.02`

therefore

The common ratio is equal to
`1.02`

the answer is

The common ratio is 1.02