Active and passive voice: rules for every tense
How the verb changes in each tense, pronoun changes, modals and imperative sentences, with SSC examples.
Study notes
Series: number and letter patterns with solved examples
Differences, squares, cubes, primes, alternating and ×+ patterns, plus letter series, with a quick checking order for SSC.
Mock Matrix · mockmatrix.in/
What a series question tests
A series is a list of numbers or letters that follows one hidden rule. You must find the rule and give the next term, a missing term or the wrong term. Most SSC series use a small set of patterns, so learn them and test them in a fixed order.
Checking order for number series
- Differences: subtract each term from the next. Look for equal, rising or repeating gaps.
- Second differences: if the first gaps are not simple, take the differences of the gaps.
- Squares and cubes: check whether terms are close to n², n³, n² ± 1 or n³ ± 1.
- Primes: check for consecutive prime numbers or their squares.
- Multiplication patterns: if terms grow fast, try ×2, ×3 or ×n with an added or subtracted number.
- Alternating series: if the terms rise and fall, split the odd and even positions into two series.
Common patterns
| Pattern | Example | Next |
|---|---|---|
| Rising difference (+2, +3, +4 …) | 4, 6, 9, 13, 18 | 24 |
| Second differences | 2, 3, 6, 12, 22 (gaps 1, 3, 6, 10) | 37 |
| n² + 1 | 2, 5, 10, 17, 26 | 37 |
| n³ − 1 | 0, 7, 26, 63, 124 | 215 |
| Primes | 11, 13, 17, 19, 23 | 29 |
| ×2 + 1 | 3, 7, 15, 31, 63 | 127 |
| ×1 + 1, ×2 + 2, ×3 + 3 … | 2, 3, 8, 27, 112 | 565 |
| Alternating | 1, 4, 3, 8, 5, 12, 7 | 16 |
Squares 1–20: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400
Cubes 1–12: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728
Primes below 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Cubes 1–12: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728
Primes below 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Wrong-term questions
Find the rule using most of the terms, then check every term against it. In 1, 4, 9, 15, 25, 36 the terms are squares, so 15 is wrong; it should be 16. Do not change the rule to fit the odd term.
Letter series
Convert letters to their positions (A = 1 … Z = 26) and treat the series as numbers. If a count goes past Z, start again at A (Z + 1 = A). Watch for these types:
- Fixed gap: B, E, H, K, N (+3 each).
- Rising gap: A, C, F, J, O (+2, +3, +4, +5).
- Backward: Z, W, T, Q, N (−3 each).
- Letter pairs: AZ, BY, CX, DW (first letter forward, second letter backward; each pair is a letter and its opposite).
- Mixed: a letter group where each position follows its own rule. Treat each position as a separate series.
Shortcut: If a number series grows roughly two times each step, test ×2 ± something first. If it grows three times, test ×3 ± something. Differences waste time on fast-growing series.
Solved examples
- Find the next term: 5, 11, 23, 47, 95, ?
Each term is ×2 + 1: 5 × 2 + 1 = 11, 11 × 2 + 1 = 23, and so on. Next = 95 × 2 + 1 = 191. - Find the next term: 4, 9, 25, 49, 121, ?
These are squares of consecutive primes: 2², 3², 5², 7², 11². The next prime is 13, so the answer is 13² = 169. - Find the next letter: C, F, J, O, ?
Positions are 3, 6, 10, 15. The gaps are +3, +4, +5, so the next gap is +6. 15 + 6 = 21, which is U.
Put this into practiceTake a free mock — rank, cutoff gap and coach report in minutes.
Start a free mock