Patterns • Topic 4 of 4

Missing Elements

Missing-element questions hand you a pattern with a gap somewhere in the middle or end and ask you to fill it. The method is the same as always -- find the rule -- but with one extra safeguard, because the gap can hide whether your rule really holds. Work out the rule from the terms you can see, then check it against both sides of the gap. Take 5, 10, ___, 20, 25: the visible terms rise by 5, and 10 + 5 = 15 while 15 + 5 = 20, so the rule survives both checks and the missing term is 15. When the gap sits between two known terms, you can also test backwards: in 7, ___, 21, 28 the rule 'add 7' gives 7 + 7 = 14, and 14 + 7 = 21 confirms it. Shape sequences work identically -- find the core, count to the gap, and read off which element of the core belongs there. The exam's favourite trap is the sequence where the obvious first guess fails the second check, so never accept a rule that only fits one gap. One consistent rule must explain every term, the missing one included.

✅ Solved examples

1. Fill the gap: 8, 16, ___, 32, 40
The visible terms increase by 8 (8, 16, ..., 32, 40). So 16 + 8 = 24, and checking forward 24 + 8 = 32 confirms the rule. The missing term is 24.
2. Fill the gap: 50, 45, 40, ___, 30
The pattern falls by 5 each step. After 40 comes 40 - 5 = 35, and 35 - 5 = 30 matches the next known term. The missing term is 35.
3. Fill the gap in the shape pattern: circle, square, triangle, circle, square, ___, circle
The core is 'circle, square, triangle' (ABC). After the second 'circle, square' the next core element is a triangle, and it is followed by a circle as shown. The missing shape is a triangle.
4. Fill the gap: 3, 6, 12, ___, 48
Each term doubles the previous one (3, 6, 12 multiply by 2). So 12 x 2 = 24, and 24 x 2 = 48 matches the last term. The missing term is 24.

✏️ Practice — try these, take hints as needed

1. Fill the gap: 11, ___, 21, 26, 31
Find the constant difference from the known terms.
Check your rule on both sides of the gap.
16 (rule: add 5)
2. Fill the gap: 100, 90, ___, 70, 60
The list is shrinking by a fixed amount.
Subtract the same number each step.
80 (rule: subtract 10)
3. Fill the gap: 2, 4, 8, ___, 32
The jumps keep growing, so try multiplication.
Each term doubles.
16 (rule: multiply by 2)
4. Fill the gap in the shape pattern: star, moon, star, moon, ___, moon
Find the repeating core first.
The core is two shapes long.
star (core: star, moon)

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
← Pattern Rules Take the chapter test →