Question

4.Identify each sequence as arithmetic or geometric AND find the common ratio or difference: -6,-3,0,3,6,…A. Arithmetic or GeometricB. Common ratio/rate: 5,20,80,320,1280,…A. Arithmetic or GeometricB. Common rate/ratio:

Answer 1

In order to check if the sequence is arithmetic, we can subtract each term by the term before. If result is always the same, the sequence is arithmetic and the difference between terms is the common rate.

The geometric sequence is similar, but we need to divide by the term before instead of subtracting.

So we have:

`\begin{gathered} A\text{.} \\ -3-(-6)=-3+6=3 \\ 0-(-3)=0+3=3 \\ 3-0=3 \\ 6-3=3 \end{gathered}`

So the first sequence is arithmetic, with the common rate equal to 3.

`\begin{gathered} B\text{.} \\ 20-5=15 \\ 80-20=60 \\ 320-80=240 \\ \ldots \end{gathered}`

The differences are not the same, so let's try dividing them now:

`\begin{gathered} (20)/(5)=4 \\ (80)/(20)=4 \\ (320)/(80)=4 \\ (1280)/(320)=4 \end{gathered}`

So the second sequence is geometric, and the common ratio is equal to 4.