Number and Alphabet Series

Series questions give a sequence with a missing term and ask what comes next (or fills the gap). AFCAT uses both number and alphabet series. The skill is pattern recognition - check a fixed checklist of rules rather than staring.

Number series - the rule checklist

1. Constant difference (AP): 3, 7, 11, 15 (+4 each).
2. Constant ratio (GP): 2, 6, 18, 54 (x3 each).
3. Squares/cubes: 1, 4, 9, 16 (n^2) or 1, 8, 27, 64 (n^3).
4. Changing difference: 2, 6, 12, 20, 30 - differences 4, 6, 8, 10 (next is 42).
5. Mixed operations: x2 +1, or alternate add/multiply.

Alphabet series

• Positions move by a fixed step: A, C, E, G (skip one, +2 each).
• Some use position numbers (EJOTY helps).
• Mixed alphanumeric: letters and numbers alternate with their own patterns.

Exam Tricks & Tips

• 🎯 First compute the differences; a constant difference means AP, a constant ratio means GP.
• 🎯 If differences aren't constant, check second differences or squares/cubes.
• 🎯 For alphabet series, convert letters to positions (A=1) and find the numeric step.
• 🎯 Suspect squares/cubes when numbers grow fast (1,4,9,16 or 1,8,27,64).
• 🎯 For "wrong term" series, find the rule the OTHER terms obey, then spot the one that breaks it.
• ❌ Common mistake: forcing a single rule on an alternating series - check whether odd and even positions follow separate patterns.

Quick recap

Run the checklist: differences (AP), ratios (GP), squares/cubes, changing differences, and alternating patterns. Convert letters to positions for alphabet series. Series is pure pattern-spotting - fast with practice.

Cover the answer, recall, then check. 11 series cards for AFCAT.

Q1. Next term: 3, 7, 11, 15, ?
A1. 19 (arithmetic progression, +4 each).

Q2. Next term: 2, 6, 18, 54, ?
A2. 162 (geometric progression, x3 each).

Q3. Next term: 2, 6, 12, 20, 30, ?
A3. 42 (differences 4, 6, 8, 10, 12).

Q4. Identify the pattern: 1, 4, 9, 16, 25.
A4. Perfect squares (n^2).

Q5. Next term: 1, 8, 27, 64, ?
A5. 125 (cubes; 5^3).

Q6. Next letter: A, C, E, G, ?
A6. I (skip one letter, +2 each).

Q7. First step in solving a number series?
A7. Compute the differences between consecutive terms.

Q8. Constant difference vs constant ratio — which series is which?
A8. Constant difference = AP; constant ratio = GP.

Q9. How do you handle an alphabet series?
A9. Convert letters to positions (A=1) and find the numeric step.

Q10. How do you solve a "find the wrong term" series?
A10. Find the rule the other terms follow, then identify the one that breaks it.

Q11. When should you check odd and even positions separately?
A11. When the series alternates between two interleaved patterns.

Series questions show a sequence with one missing or wrong term and ask you to continue the pattern. They test pattern recognition under time pressure — and reward a fixed checklist of the patterns setters actually use, so you stop guessing and start diagnosing.

Core idea / what this tests: whether you can identify the rule generating a number or letter sequence (arithmetic, geometric, alternating, positional) and use it to find the missing or odd term.

Deep explanation

Beginner — check the differences first

For a number series, compute the differences between consecutive terms. Constant difference → arithmetic (2,5,8,11: +3). Constant ratio → geometric (3,6,12,24: ×2). If differences themselves form a pattern, that is a second-level clue.

Intermediate — the pattern checklist

Run every series through these:

Pattern	Signature
+/− constant	equal differences
×/÷ constant	equal ratios
Squares/cubes	1,4,9,16 or 1,8,27,64
+n increasing	+2,+4,+6,+8 (second difference constant)
Alternating	two interleaved series
Prime/Fibonacci	2,3,5,7... or each = sum of previous two

Advanced — alphabet and mixed series

• Alphabet series use letter positions: skip patterns (A, C, E, G = +2) or reverse jumps. Convert letters to numbers (EJOTY) to expose the arithmetic.
• Alternating series hide two sequences: odd positions follow one rule, even positions another (e.g. 2, 100, 4, 95, 6, 90 → +2 and −5 interleaved).
• Wrong-term questions ask which entry breaks the rule — establish the rule from the majority, then spot the outlier. Always confirm your rule fits at least three terms before trusting it.

Worked example

Q. Find the next term: 3, 6, 12, 24, ?

Check ratios: 6/3 = 2, 12/6 = 2, 24/12 = 2 — a constant ratio, so it is geometric with ×2. Next term = 24 × 2 = 48.

Answer: 48. Differences alone (3,6,12) look irregular; testing the ratio revealed the clean rule. Always try both difference and ratio.

AFCAT relevance

Number and letter series recur in AFCAT reasoning and are quick once the pattern is spotted. The diagnostic checklist prevents the time-sink of random trial, and since a mis-identified rule leads to a confident wrong answer, disciplined verification protects against negative marking.

Speed tricks and shortcuts

• Compute differences first, then ratios if differences do not settle.
• Watch for squares/cubes near 1,4,9,16 or 1,8,27,64.
• Suspect an alternating series when terms zig-zag up and down.
• Convert letters to numbers (EJOTY) to see alphabet-series arithmetic.

Worked Example

Problem: Find the next number in the series: 2, 6, 12, 20, 30, ?

Solution:
Look at the differences between consecutive terms:
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 should be 12.
Next term = 30 + 12 = 42.

Confirm with a direct pattern: each term equals n × (n + 1):
1×2 = 2, 2×3 = 6, 3×4 = 12, 4×5 = 20, 5×6 = 30, and 6×7 = 42. ✓

Both methods give 42.

Answer: 42.