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

3. 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,... 10 th ?

4. The tenth term is 28

5. Now find the one-hundredth term: 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16,... 100 th ?

6. 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,... 100 th ?

7. 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,... 1000 th ?

8. 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,... 1000 th ?

9. 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,... 1000 th ?

10. ... onto the number itself. 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16,... 1000 th ?

11. Now 4 will map onto 10, 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16,... 1000 th ? and so forth. 6 will map onto 16,

12. 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,... 1000 th ? to correspond with a y-value of 16.

13. How can we write the equation? 1, 1 st 2 nd 3 rd 4 th 5 th 6 th 4,7,10,13,16,... 1000 th ?

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

15. We can start with an equation,

16. and see what pattern develops.

17. each time x What happens to y increases by 1?

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

19. Look at the equation we used to get those numbers.

20. Notice the 4.

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

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

24. 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,... 100 th ?

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

26. We can get y by multiplying x by 3,

27. and then adding or subtracting some number.

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

29. so we get,

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

31. Now we can complete the equation.

32. 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,... 100 th ?

33. These are the steps we took to write the equation:

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

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

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

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

40. 4.Write the final equation.

41. Write the equation: 1. 2. 3.

42. Answers: 1. 2. 3. * Press Enter

43. 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?