Find the next three terms in the pattern: 1, 4, 7,...

Find the tenth term in the pattern: 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

The tenth term is 28

Now find the one-hundredth term: 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

You don’t really want to write out 100 terms, do you? 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

If so, go ahead and find the 1,000 th term. 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

If not, we need to find a better way. 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

One way would be to write an equation which maps the number’s rank... 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

... onto the number itself. 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

Now 4 will map onto 10, 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ? and so forth. 6 will map onto 16,

And 6 will be an x-value 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ? to correspond with a y-value of 16.

How can we write the equation? 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

.drawkcab krow s’teLLet’s work backward..drawkcab krow s’teL

We can start with an equation,

and see what pattern develops.

each time x What happens to y increases by 1?

Each time x increases by 1, y increases by 4.

Look at the equation we used to get those numbers.

Notice the 4.

Let’s try this equation: Predict what y will do as x increases by 1.

There is a pattern working here. The amount y changes each time x increases by 1 is part of the equation.

So if we go back to the pattern we started with: 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

We see that y increases by 3 each time x increases by 1, and we can start writing the equation.

We can get y by multiplying x by 3,

and then adding or subtracting some number.

When we use 1 for x, we know that y is also 1,

so we get,

What does b have to be to make the equation true?

Now we can complete the equation.

What is the 100 th term in the pattern? 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16, th ?

These are the steps we took to write the equation:

1.Find the change in y each time x changes by 1.

2.Begin writing the equation,, using the change in y as m.

3.Calculate b, using the numbers from our table.

3.Calculate b, using the numbers from the table.

4.Write the final equation.

Write the equation:

Answers: * Press Enter

3. Did you notice that x is increasing by 2, not one? If y increases 10 every time x increases 2, what is the increase in y as x increases 1?