Introduction to Number and Letter Series

Number and Letter Series

A series is a sequence of numbers or letters that follows a fixed rule. Your job is to find the rule and then the next or missing term.

Common number-series patterns

• Constant difference: 5, 9, 13, 17 → +4 each time.
• Increasing difference: 2, 6, 12, 20, 30 → differences 4, 6, 8, 10 → next 42.
• Multiplication/Division: 3, 9, 27, 81 → ×3.
• Squares/Cubes: 1, 4, 9, 16 (n²); 1, 8, 27, 64 (n³); n² ± 1 variants.
• Mixed operations: ×2 +1, ×2 +1 …
• Alternate series: two series interleaved at odd and even positions.

Letter series

Convert letters to positions: A=1 … Z=26 (remember EJOTY = 5, 10, 15, 20, 25).

• A, C, F, J, O → gaps +2, +3, +4, +5 → next +6 = U.
• AZ, BY, CX → first letter forward, second backward → DW.
• Opposite pairs: A–Z, B–Y, C–X (sum = 27).

Step-by-step approach

1. Look at differences between consecutive terms.
2. If differences don't settle, try ratios, squares/cubes, or alternate terms.
3. For letters, write position numbers and treat it as a number series.
4. Verify the rule on every term before answering.

Analogy

A series is like the stations on a railway line with a regular timetable. If trains leave at 6:00, 6:15, 6:30, 6:45 you instantly know the next is 7:00 — the rule is "+15 minutes". Some routes are trickier: the gap grows by 5 minutes each time (like 2, 6, 12, 20 where gaps grow by 2). Letter series work the same — just replace station names with their platform numbers (A=1, B=2 …) and read the timetable.