Number Series Completion

• How to spot the hidden rule in a sequence of numbers.
• Common series types: constant difference, constant ratio, squares, increasing gaps, Fibonacci-style sums, and alternating operations.
• A step-by-step method to predict the next term confidently, even under exam time pressure.

1. Constant difference (Arithmetic Progression) — the same number is added (or subtracted) every time, e.g. 3, 6, 9, 12 (+3 each time).
2. Constant ratio (Geometric Progression) — each term is multiplied by the same factor, e.g. 2, 6, 18, 54 (×3 each time).
3. Squares / special number patterns — terms follow n², n³, or similar known patterns.
4. Increasing/decreasing gap series — the difference between terms itself changes in a pattern (e.g. +2, +3, +4, +5).
5. Combined operations — two operations alternate, such as "+3" then "×2" repeating.
6. Fibonacci-style series — each term is the sum of the previous two terms.

Series: 3, 6, 12, 24, ?

Step 1 — find the differences: 3, 6, 9 are not equal, so it is not a simple A.P.
Step 2 — check ratios: 6/3 = 2, 12/6 = 2, 24/12 = 2 → constant ratio of 2
Step 3 — apply the rule: next term = 24 × 2 = 48

• Assuming every series is "add a constant" without checking ratios or squares first.
• Missing that the difference itself forms a series (increasing gap pattern).
• Forgetting to double-check by applying the found rule backward to confirm all given terms fit.

• Is 2, 4, 8, 16 an arithmetic or a geometric series?
• What is the next term of 1, 4, 9, 16, ?
• Find the next term of 2, 3, 5, 8, 13, ? (hint: Fibonacci-style).

Open the Practice tab for graded questions on Number Series Completion.