Question

Jane graphs these ordered pairs(1,4),(5,6),(9,8),(13,10)If the pattern continues what will be the next ordered pair be?

Answer 1

Given the following ordered pairs below

`(1,4),(5,6),(9,8),(13,10),(p,q)`

Where p and q are the next pair we want to find.

By observation, we can deduce that the x values sequence is;

`\begin{gathered} 1,5,9,13 \\ \text{The common difference is +4} \\ \text{thus, } \\ p=13+4=17 \end{gathered}`

We can also deduce the y-values sequence to be:

`\begin{gathered} 4,6,8,10 \\ \text{The common difference is +2} \\ \text{Thus,} \\ q=10+2=12 \end{gathered}`

Hence, the next ordered pair is (17,12)