Number patternsGrowing by a factor
Name: Date:
Find the missing number in each pattern.
11, , 9, 27
23, 6, , 24
34, , 16, 32
42, 4, , 16
52, , 18, 54
64, , 36, 108
71, 3, , 27
83, , 12, 24
92, 6, , 54
103, 9, , 81
Multiplying number patterns worksheets
Some sequences do not add the same amount — they multiply by it, so they grow fast. These free printable worksheets show a sequence that doubles or triples with one number missing, and ask a child to find the factor and fill the gap.
Kid stuck on one? You don’t just get the sheet.
Multiplying number patterns
The answer key prints on a separate page.
What's on this sheet
Each sequence grows by a fixed factor rather than a fixed step: 2, 6, 18, 54 triples every time. The tell is the speed — the jumps get bigger and bigger, which is what says to test multiplying instead of adding. Dividing one term by the one before it uncovers the factor, and that division is the check a child runs on every pair.
Why this sheet works
The blank sits inside the sequence, so filling it means multiplying forward from the term before and confirming it divides cleanly into the term after. A child who only continues the pattern from the front can land on a number that does not fit the far side, which is exactly what the interior blank is there to catch.
How this one works
One question from this sheet, worked through a step at a time.
1, ?, 9, 27
1?927
1?927
1?927
13927
- Find the rule first, from two numbers you can actually see — never from the gap.
- 9 to 27 is × 3. One pair is only a guess — the number after the gap will confirm it.
- Now apply it to the gap: 1 × 3 = 3.
- Check it against the number already after the gap: 3 × 3 = 9, which is what is there. The missing number is 3.