# Number and Letter Series — How to Find the Pattern Fast

Source: https://skills101.in/learn/reasoning/number-and-letter-series — Skills101 free tutorial (Logical Reasoning). Updated 2026-11-09.

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

![Series 3, 5, 9, 15, 23, ? — the differences are 2, 4, 6, 8, so the next difference is 10 and the answer is 33](https://skills101.in/learn-img/reasoning/series-differences.svg)

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.

![Alphabet with positions 1 to 26; E, J, O, T, Y highlighted at 5, 10, 15, 20, 25. Opposite letters add up to 27](https://skills101.in/learn-img/reasoning/alphabet-positions.svg)

### 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.


Practice quiz and free certificate: https://skills101.in/learn/reasoning/number-and-letter-series