Number & Alphabet Series
Series questions are a search problem: you are looking for the rule, and there is a fixed order worth searching in. Checking differences first, then ratios, then squares and cubes, then alternating patterns will find the rule in the large majority of questions.
Updated 19 September 2026 · Present in essentially every aptitude paper.
How to think about number & alphabet series
Search in a fixed order
Take consecutive differences first. If those are constant you have an arithmetic series; if the differences themselves form a pattern, that is a second-order series. Only if differences fail should you try ratios, then squares and cubes, then alternating or interleaved sequences. Searching in a set order is much faster than staring.
Recognise the standard sequences on sight
Squares 1, 4, 9, 16, 25; cubes 1, 8, 27, 64, 125; primes 2, 3, 5, 7, 11; Fibonacci-style where each term is the sum of the previous two. A term like 121 or 169 should immediately suggest squares.
Two series can be interleaved
If nothing works on consecutive terms, check the odd-numbered and even-numbered positions as two separate series. Alternating series are common precisely because they defeat the usual difference check.
Alphabet series use positions
Convert letters to their positions and the problem becomes a number series. Do not try to see the pattern in the letters themselves.
Formulas and shortcuts
- Arithmetic series
Each term = previous + d (constant difference) - Geometric series
Each term = previous × r (constant ratio) - Second-order
The differences themselves form a pattern - Fibonacci style
Each term = sum of the two before it - Squares
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 - Cubes
1, 8, 27, 64, 125, 216, 343
Solved examples
Q1. Find the next term: 2, 6, 12, 20, 30, ?
- Take differences: 6−2=4, 12−6=6, 20−12=8, 30−20=10
- The differences are 4, 6, 8, 10 — increasing by 2 each time, so the next difference is 12.
- Next term = 30 + 12
Answer: 42
These are also n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7 = 42. Two routes, same answer.
Q2. Find the next term: 3, 6, 12, 24, ?
- Differences are 3, 6, 12 — not constant, and they double, which hints at a ratio.
- Check ratios: 6/3 = 2, 12/6 = 2, 24/12 = 2. Constant ratio of 2.
- Next = 24 × 2
Answer: 48
Q3. Find the missing term: 1, 4, 9, 16, 25, ?
- Differences are 3, 5, 7, 9 — odd numbers increasing by 2, which is the signature of squares.
- Indeed the terms are 1², 2², 3², 4², 5².
- The next term is 6².
Answer: 36
Practice questions with answers
1. Find the next term: 5, 10, 20, 40, ?
Answer: C. 80 — Each term doubles. 40 × 2 = 80.
2. Find the next term: 2, 5, 10, 17, 26, ?
Answer: B. 37 — Differences are 3, 5, 7, 9, so the next is 11. 26 + 11 = 37. (The terms are n² + 1.)
3. Find the next term: 1, 1, 2, 3, 5, 8, ?
Answer: C. 13 — Fibonacci — each term is the sum of the two before it. 5 + 8 = 13.
4. Find the next term: 1, 8, 27, 64, ?
Answer: C. 125 — These are cubes: 1³, 2³, 3³, 4³. Next is 5³ = 125.
5. Find the next letter: A, C, E, G, ?
Answer: B. I — Positions 1, 3, 5, 7 — increasing by 2. Next is position 9, which is I.
6. Find the odd one out: 4, 9, 16, 24, 36
Answer: C. 24 — All are perfect squares (2², 3², 4², 6²) except 24.
7. Find the next term: 100, 81, 64, 49, ?
Answer: C. 36 — Descending squares: 10², 9², 8², 7². Next is 6² = 36.
Where marks get lost
- Giving up after the difference check instead of moving on to ratios and squares.
- Missing an interleaved series because only consecutive terms were compared.
- Trying to read alphabet patterns as letters instead of converting to positions.
- Finding a rule that fits the first two terms and not testing it against the rest.
Reading is not practising.
Run a timed set on number & alphabet series and see which step you actually lose time on. Free, no card needed.
Start a timed set