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Series Completion
Series Completion · 7 Sections

Series Completion

Master number, letter and alphanumeric series — arithmetic progressions, geometric progressions, difference tables, prime and Fibonacci patterns, and every trick tested in SSC CGL, Railways, UPSC and CAT.

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Section 1 of 7

📊 Introduction — Difference Table Approach

A series is an ordered list of numbers or letters following a definite rule. Your job is to find the next term, a missing term, or the wrong term that breaks the pattern. The single most powerful technique for any series is building a difference table.

The Difference Table MethodWrite the series in Row 1. Below it write Row 2: each cell = (next term − current term). Repeat to get Row 3 (differences of differences). If any row becomes constant, you have found the rule. Work back up to find the missing term.
Row 1 (terms):2  5  10  17  26  ?
Row 2 (1st diff):3  5  7  9  → next = 11odd numbers: constant 2nd diff
Row 3 (2nd diff):2  2  2  2  → constant!
Answer:26 + 11 = 37
🔢Series SolverInteractive pattern explorer
AP: d = 31/10
Series
2581114→?= 17
Difference Table
RowT1T2T3T4T5T6
Terms258111417
1st diff+3+3+3+3+3
2nd diff0000
Ratio2.501.601.381.271.21
Pattern: Arithmetic — common difference 3
Exam tip: Always calculate first differences before guessing. If the first differences themselves form an AP or GP, you have a second-order series. If they form a pattern of squares or cubes, look for n² or n³.

A series where the first differences are constant is an Arithmetic Progression. A series where the ratio between terms is constant is a Geometric Progression. When the first differences form an AP, the second differences become constant — this is a second-order difference series.

The next term is in the series 2, 5, 10, 17, 26, ? (use the difference table above).

If the first differences of a series are 2, 4, 8, 16, they form a with ratio 2.

In the series 1, 4, 9, 16, 25, the second differences are because the first differences 3, 5, 7, 9... form an AP with d = 2.

📝Practice Questions

Q1What is the next term in the series: 3, 6, 9, 12, ?

Q2In the series 2, 5, 10, 17, 26, ?, what is the pattern of first differences?

Q3The first differences of a series are 2, 4, 8, 16. What type of progression are the differences?

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Section 2 of 7

🔢 Arithmetic & Geometric Number Series

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Section 3 of 7

📐 Difference-of-Difference Series

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Section 4 of 7

✨ Special Number Series

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Section 5 of 7

🔤 Letter Series

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Section 6 of 7

🔡 Alphanumeric Series

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Section 7 of 7

🔍 Wrong Term & Missing Term

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