How is this different from the number sequence puzzle generator?

That one hides the last term and asks what comes next. This hides one from the middle, which is a genuinely different exercise: the missing value is bracketed by known ones, so it can be found by inverting the rule from the right as well as applying it from the left. Students who are fluent at one are frequently not fluent at the other, which is the reason both exist.

Why is the gap never at the start or end?

A gap at the end is the next-term puzzle, which has its own page. A gap at the start removes the anchor the rule is measured from and makes several rule families unidentifiable rather than merely harder.

Can I check my answer without revealing it?

Yes, and it is the best habit this exercise builds: work it out from the left, then again from the right, and see whether they agree. Two agreeing answers are almost certainly correct, and two that disagree tell you the rule was misread.

Missing Number Puzzle Generator

Finding the missing number in the middle of a sequence is not the same task as finding the next one, and treating them as the same is why students who are fluent at one stall on the other. With a gap in the middle you can approach from both directions, and the arithmetic of working backwards is genuinely different from working forwards.

Difficulty

Number of terms

Between 4 and 10. Short sequences are much more ambiguous.

Restrict to particular rule families

Leave all unticked to draw from whatever the difficulty allows. Working through one family at a time is far more useful for teaching than a mixed set.

Add the same amount each time

Multiply by the same amount each time

Square numbers

Triangular numbers

Each term is the sum of the two before it

Two rules alternating

The gap grows by a fixed amount each time

Seed (optional)

Makes the puzzle reproducible, so a worksheet can be printed twice.

Your sequence will appear here.

What this generator does

Generates a sequence from a known rule and hides one term from the interior rather than the end. That single change makes it a different exercise: the missing term is bracketed by known values, so it can be found by working forwards from the left, backwards from the right, or by using both as a check. Working backwards means inverting the rule — subtracting where the rule adds, dividing where it multiplies — which is a distinct skill and one that transfers directly to solving equations.

How to use this tool

Choose a difficulty and a sequence length.
Press Generate. One term from the interior will be hidden.
Work it out from the terms on either side.
Reveal to check the answer and see the rule.

Understanding the controls

Difficulty: Easy uses constant differences and ratios with small numbers, where working backwards is one subtraction. Hard adds rules where inverting is genuinely awkward — an alternating rule inverts differently depending on which position the gap is in.
Number of terms: Longer sequences give more context on both sides of the gap, which makes the rule easier to spot and the arithmetic no easier. Six to eight is a good working range.
Rule families: Restrict to what you are teaching. Constant difference is where to start, because its inverse is a single subtraction; ratios are the natural next step, since inverting a multiplication is a division.

Worked examples

Constant difference: 4, 11, ?, 25, 32 — the gap is 7, so the missing term is 18.
Working backwards: 3, 6, 12, ?, 48 — doubling forwards gives 24, and halving 48 backwards confirms it.
Both directions agreeing: The value from the left and the value from the right must match. Where they do not, the rule has been misread.
Harder: 2, 9, 18, ?, 40 — the gap grows by 2 each time, so the missing term is 29.

Common use cases

Primary and lower-secondary maths practice on number patterns
Teaching inverse operations, which is what working backwards actually is
Reasoning-test preparation, where interior gaps are a standard variant
A quick starter that takes two minutes and needs no preparation
Assessing whether a student understands a rule or has only memorised forward counting

How this generator works

The sequence is generated forwards from a chosen rule, exactly as the next-term generator does, and then one interior position is hidden. Interior means never the first or last term, which matters: hiding the last term is a different puzzle and hiding the first removes the anchor that makes the rule findable at all. Because both neighbours of the gap are visible, the puzzle is always solvable by inverting the rule once, which is the property that makes it a teaching exercise rather than a guess.

Randomness and fairness

The rule, its parameters and which interior position is hidden are all drawn with the browser's cryptographic random number generator. The terms themselves are not random at all — they follow from the rule, which is what lets the tool guarantee the puzzle is solvable from either side. A seed reproduces a worksheet using a deterministic generator that is not cryptographically secure, which is the property that makes reprinting possible.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

The rule applies consistently across the whole sequence, including across the gap.
Exactly one term is missing.

Limitations and good to know

As with any sequence puzzle, the rule shown is one that fits rather than the only one that could. A student with a different rule that fits every visible term has answered correctly.
The gap is never the first or last term, by design. Those are different puzzles and the next-term generator covers one of them.
Only the same seven rule families are covered — no primes, digit patterns or word-based sequences.
It cannot mark an answer, only show the one its rule produces.
With a very short sequence and a gap in the middle, there is little context on either side and the puzzle becomes considerably more ambiguous.

Common mistakes

Only working forwards: Check from the right as well. If the two answers disagree you have the rule wrong, and finding that out from the sequence itself is the most useful thing this exercise teaches.
Assuming the gap between neighbours of the missing term is the rule's step: The visible neighbours of a gap are two steps apart, not one. With a constant difference the gap between them is double the step, and forgetting that is the single most common error here.
Treating it as the same exercise as 'what comes next': It is not. Working backwards requires inverting the rule, and students fluent at forward counting frequently cannot do it. That gap is exactly what this is for.

Practical tips

Ask for the answer twice — once from the left, once from the right — and for both to be shown. Agreeing answers are self-marking.
Follow it with the same rule as a next-term question. The comparison makes the difference between the two skills obvious.
For students who are stuck, cover everything to the right of the gap. It reduces to a forward problem and usually unblocks them immediately.

Troubleshooting

The two directions give different answers: The rule has been misread, which is useful information rather than a fault. Recheck the differences across the whole sequence rather than just next to the gap.
The gap is too near the start to have context: It is never the first term, but it can be the second. Use a longer sequence — the position is drawn from the interior, so more terms means more context on average.

Privacy and your data

Nothing is entered and nothing is stored. Puzzles are generated in your browser, nothing is uploaded or written into the page address, and analytics records only that the tool was used along with the difficulty — never a puzzle.

Frequently asked questions

How is this different from the number sequence puzzle generator?: That one hides the last term and asks what comes next. This hides one from the middle, which is a genuinely different exercise: the missing value is bracketed by known ones, so it can be found by inverting the rule from the right as well as applying it from the left. Students who are fluent at one are frequently not fluent at the other, which is the reason both exist.
Why is the gap never at the start or end?: A gap at the end is the next-term puzzle, which has its own page. A gap at the start removes the anchor the rule is measured from and makes several rule families unidentifiable rather than merely harder.
Can I check my answer without revealing it?: Yes, and it is the best habit this exercise builds: work it out from the left, then again from the right, and see whether they agree. Two agreeing answers are almost certainly correct, and two that disagree tell you the rule was misread.