Number and Alphabet Series
About 6 min · Logical Reasoning · English
Time worked out from the lesson's 326 words at 150 words a minute, plus a minute for each question.
Number and alphabet series problems are part of the SOF IMO Logical Reasoning section. These questions test your ability to identify patterns and relationships between consecutive terms in a sequence of numbers, letters, or a combination of both. You may be given 4–6 terms and asked to find the next term or a missing element in the middle.
Key ideas
- Arithmetic progression: Each term increases or decreases by a constant difference (e.g., 3, 7, 11, 15 → difference +4).
- Geometric progression: Each term is multiplied or divided by a constant ratio (e.g., 2, 6, 18, 54 → ratio ×3).
- Square/cube sequences: Terms follow n², n³ or related patterns (e.g., 1, 4, 9, 16, 25 are squares of 1, 2, 3, 4, 5).
- Prime number series: Sequence of consecutive primes (2, 3, 5, 7, 11, 13...).
- Alternating patterns: Two interleaved sub-series, each with its own rule (e.g., odd positions increase by 3, even positions double).
Watch out for
- Assuming single pattern when alternating exists → Always check if odd and even positions follow separate rules. If a single arithmetic/geometric rule fails, split the series.
- Forgetting zero in position counting → When converting letters to numbers, A=1 not 0. Students often miscount by one.
- Miscalculating squares and cubes → 7²=49 not 48; 4³=64 not 54. Memorise up to 10² and 8³ to avoid arithmetic errors under pressure.
Quick reference
- Arithmetic series: constant difference between terms → add/subtract same number each time.
- Geometric series: constant ratio → multiply/divide by same number each time.
- Alternating: split odd/even positions → solve each sub-series independently.
- Squares/cubes: if terms grow fast, test n², n³ or n²+n patterns immediately.
- Alphabet: convert to numbers (A=1...Z=26), find numeric pattern, convert back.
Check yourself: 3 questions
1. Find the next term in the series: 3, 7, 15, 31, 63, ?
2. Find the missing term in the alphabet series: B, E, I, N, T, ?
3. In the series 2, 6, 12, 20, 30, 42, the 10th term is:
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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