Finding the rule behind a table

Difficulty Starter · Set 9e5yaa

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1
x goes 1, 2, 3, 4 and the rule gives 3, 5, 7, 9. What does the rule multiply x by?
2
x goes 1, 2, 3, 4 and the rule gives 5, 8, 11, 14. What does the rule multiply x by?
3
x goes 1, 2, 3, 4 and the rule gives 9, 12, 15, 18. What does the rule multiply x by?
4
x goes 1, 2, 3, 4 and the rule gives 8, 11, 14, 17. What does the rule multiply x by?
5
x goes 1, 2, 3, 4 and the rule gives 10, 13, 16, 19. What does the rule multiply x by?
6
x goes 1, 2, 3, 4 and the rule gives 8, 10, 12, 14. What does the rule multiply x by?
7
x goes 1, 2, 3, 4 and the rule gives 12, 15, 18, 21. What does the rule multiply x by?
8
x goes 1, 2, 3, 4 and the rule gives 8, 11, 14, 17. What does the rule multiply x by?
9
x goes 1, 2, 3, 4 and the rule gives 10, 13, 16, 19. What does the rule multiply x by?
10
x goes 1, 2, 3, 4 and the rule gives 3, 5, 7, 9. What does the rule multiply x by?
11
x goes 1, 2, 3, 4 and the rule gives 4, 7, 10, 13. What does the rule multiply x by?
12
x goes 1, 2, 3, 4 and the rule gives 4, 6, 8, 10. What does the rule multiply x by?
13
x goes 1, 2, 3, 4 and the rule gives 3, 5, 7, 9. What does the rule multiply x by?
14
x goes 1, 2, 3, 4 and the rule gives 4, 7, 10, 13. What does the rule multiply x by?
15
x goes 1, 2, 3, 4 and the rule gives 12, 15, 18, 21. What does the rule multiply x by?
16
x goes 1, 2, 3, 4 and the rule gives 6, 8, 10, 12. What does the rule multiply x by?
17
x goes 1, 2, 3, 4 and the rule gives 4, 7, 10, 13. What does the rule multiply x by?
18
x goes 1, 2, 3, 4 and the rule gives 6, 9, 12, 15. What does the rule multiply x by?
19
x goes 1, 2, 3, 4 and the rule gives 7, 9, 11, 13. What does the rule multiply x by?
20
x goes 1, 2, 3, 4 and the rule gives 9, 11, 13, 15. What does the rule multiply x by?

What is in this set

The numbers in this set run from 1 to 21.
A careful solution takes 2 written steps on average.
The mistake this set invites most often, in 100% of the problems: the first output was read off as the multiplier; the multiplier is the step between one output and the next.
Answers are a whole number.

Drawing 240 problems from this page produced 18 different ones, 8% — so a sheet of 20 will come back to a problem you have seen — there are only so many sensible ones of this kind.

The same skill, harder or easier

We would put this in front of a grade 7 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.