Logical Reasoning · Lesson 1 of 13 · Updated ·
Number and Letter Series — How to Find the Pattern Fast
A series question gives a list with a missing (or wrong) term. Your job is to find the rule. There are only about ten common rules, so check them in a fixed order.
1. Start with the differences
Write the difference between each pair of neighbours. If the differences show a pattern (constant, +2 each time, doubling, squares…), you are done.
Example 1
7, 11, 19, 35, 67, ?
Differences: 4, 8, 16, 32 (doubling) → next is 64 → 67 + 64 = 131.
If the differences don't show a pattern, take differences of the differences (second level).
2. The checklist
| Check | Looks like | Example |
|---|---|---|
| Constant difference | +5, +5, +5 | 4, 9, 14, 19 |
| Differences in a pattern | +2, +4, +6 | 3, 5, 9, 15, 23 |
| Multiply | × 2, × 3 | 2, 6, 18, 54 |
| Multiply and add | × 2 + 1 | 3, 7, 15, 31 |
| Squares / cubes | n², n³, n² + 1 | 2, 5, 10, 17, 26 |
| Primes | prime numbers, or primes + 1 | 3, 4, 6, 8, 12, 14 (primes + 1) |
| Alternating (two series mixed) | odd places and even places | 1, 10, 2, 20, 3, 30 |
| Fibonacci-like | each term = sum of previous two | 1, 2, 3, 5, 8, 13 |
Tip: if numbers grow slowly, think addition. If they grow fast, think multiplication or powers. If they go up and down, think alternating.
Example 2 — multiply and add
2, 5, 11, 23, 47, ? → each term × 2 + 1 → 47 × 2 + 1 = 95.
Example 3 — squares
0, 3, 8, 15, 24, ? → n² − 1 for n = 1, 2, 3… → 6² − 1 = 35.
Example 4 — alternating
5, 12, 10, 24, 15, 48, ? → odd places 5, 10, 15 (+5); even places 12, 24, 48 (× 2) → next odd place = 20.
Example 5 — find the wrong number
3, 8, 15, 24, 34, 48
Expected n² − 1: 3, 8, 15, 24, 35, 48 → 34 is wrong.
3. Letter series
Convert letters to positions. Learn EJOTY (5, 10, 15, 20, 25) to find any letter fast.
Example 6
B, E, H, K, ? → 2, 5, 8, 11 (+3) → 14 = N.
Example 7
AZ, BY, CX, ? → first letter forward, second letter backward (opposite pairs) → DW.
Example 8 — letter groups
ACE, FHJ, KMO, ? → each group skips one letter; groups start A, F, K (+5) → PRT.
Common mistakes
- Trying random ideas instead of the checklist. Always do differences first.
- Missing an alternating series because you only look at neighbours.
- Counting letter positions on your fingers — use EJOTY.
Quick recap
- Differences first, then second differences.
- Slow growth → add; fast growth → multiply or powers; up and down → alternating.
- Letters: convert to numbers; EJOTY; opposite letters add to 27.