Number & Alphabet Series • Topic 1 of 4

Number Series

Take first differences between consecutive terms. If they are constant it is an AP; if they grow steadily look at second differences; if terms multiply, find the ratio. Squares, cubes, and 'square ±1' patterns are SSC staples; for longer series test alternate terms.

Write the differences underneath

The fastest first move is to note the gap between each pair of terms. A constant gap is an arithmetic progression; a growing gap points to a second-level pattern.

25811 +3+3+3 Constant difference of 3 → next term = 11 + 3 = 14
Difference arcs reveal the rule at a glance: here a steady +3 (an AP).

The scan order

  1. First differences constant? → AP (add a fixed number).
  2. Differences growing by a fixed amount? → second-difference pattern (e.g., +1, +2, +3…).
  3. Ratio constant? → GP (multiply by a fixed number).
  4. Squares/cubes/primes? Memorise squares to 20 and cubes to 12 — they appear constantly.
  5. Still stuck? Test alternate terms — two series may be interleaved.

✅ Solved examples

1. Next term: 2, 5, 8, 11, ?
Constant difference +3. 11 + 3 = 14.
2. Next: 3, 6, 12, 24, ?
Ratio ×2. 24 × 2 = 48.
3. Next: 2, 6, 12, 20, ?
Differences 4,6,8 → next +10. 20 + 10 = 30.
4. Next: 1, 4, 9, 16, ?
Squares: 5^2 = 25.

✏️ Practice — try these, take hints as needed

1. Next: 5, 10, 20, 40, ?
Ratio.
×2.
—
80
2. Next: 7, 10, 13, 16, ?
+3.
—
—
19
3. Next: 1, 8, 27, 64, ?
Cubes.
5^3.
—
125
4. Next: 3, 4, 6, 9, 13, ?
Diffs 1,2,3,4.
next +5.
—
18
5. Next: 2, 3, 5, 7, 11, ?
Primes.
after 11.
—
13

📝 Topic test — 8 questions

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