शृंखला

हिंदी में पढ़ें

Series — Crack the Pattern, Crack the Exam

1. What You Will Learn

A "series" question gives you a sequence of numbers, letters, or figures that follow a hidden rule, and asks you to find the missing or next term. By the end of this chapter you will be able to:

• Recognise the standard types of number series (arithmetic, geometric, squares, cubes, mixed operations).
• Solve alphabet and alpha-numeric series using letter positions.
• Handle "wrong term in the series" questions.
• Apply a quick checking order in the exam so you do not waste time.

Series questions appear in almost every government exam's reasoning section — SSC (CGL, CHSL, GD, MTS), RRB (NTPC, Group D), Bank exams (IBPS, SBI) and State exams. They are scoring because the method is fixed: find the rule, apply the rule.

2. Number Series — The Main Types

2.1 Arithmetic Series (constant difference)

Each term changes by a fixed number.

Example: 4, 9, 14, 19, ?
Rule: +5 each time → next term = 24.

The difference itself can also form a pattern:

Example: 3, 5, 9, 17, 33, ?
Differences: 2, 4, 8, 16 (doubling) → next difference 32 → answer = 65.

2.2 Geometric Series (constant ratio)

Each term is multiplied (or divided) by a fixed number.

Example: 5, 15, 45, 135, ?
Rule: ×3 each time → next term = 405.

2.3 Square and Cube Series

Terms are based on squares (n²) or cubes (n³), sometimes with a small addition or subtraction.

Example: 1, 4, 9, 16, 25, ? → squares of 1, 2, 3, 4, 5 → next = 6² = 36.

Example: 2, 5, 10, 17, 26, ? → these are n² + 1 (1+1, 4+1, 9+1, …) → next = 36 + 1 = 37.

Tip: Memorise squares up to 25² = 625 and cubes up to 12³ = 1728. Most exam series use numbers from this range.

2.4 Mixed / Alternating Operations

Two operations alternate, or the multiplier itself grows.

Example: 7, 14, 13, 26, 25, ?
Rule: ×2, −1, ×2, −1 → next = 25 × 2 = 50.

Example: 2, 6, 24, 120, ?
Rule: ×3, ×4, ×5 → next = 120 × 6 = 720.

2.5 Two Interleaved Series

Odd-position terms follow one rule; even-position terms follow another.

Example: 1, 10, 3, 20, 5, 30, ?
Odd positions: 1, 3, 5 (+2). Even positions: 10, 20, 30 (+10) → next (odd position) = 7.

2.6 Prime Numbers and Special Sequences

Example: 2, 3, 5, 7, 11, 13, ? → consecutive primes → next = 17.

3. Alphabet Series

Write down letter positions first: A=1, B=2, … M=13, N=14, … Z=26. Remembering "EJOTY" (E=5, J=10, O=15, T=20, Y=25) helps you locate any letter quickly.

3.1 Constant Gap

Example: C, F, I, L, ?
Positions: 3, 6, 9, 12 (+3) → next = 15 = O.

3.2 Increasing Gap

Example: A, C, F, J, ?
Gaps: +2, +3, +4 → next gap +5 → 10 + 5 = 15 = O.

3.3 Letter Groups

Example: AZ, BY, CX, DW, ?
First letters: A, B, C, D (+1). Second letters: Z, Y, X, W (−1) → next = EV.

3.4 Alpha-Numeric Series

Example: Z1A, X2D, V3G, T4J, ?
Letters: Z, X, V, T (−2 each). Numbers: 1, 2, 3, 4 (+1). End letters: A, D, G, J (+3) → next = R5M.

4. Wrong Term in the Series

Here one term breaks the rule. Find the rule from the majority of terms, then identify the misfit.

Example: 2, 6, 12, 20, 32, 42
Check: differences should be 4, 6, 8, 10, 12 (i.e., terms n² + n: 2, 6, 12, 20, 30, 42). The term 32 is wrong; it should be 30.

Method: Compute differences (or ratios) for the whole row. The place where the pattern breaks twice (once entering, once leaving) marks the wrong term.

5. A Quick Checking Order for the Exam

When you see a number series, test in this order — it covers most exam questions:

1. Differences — constant, or themselves forming a pattern (+2, +4, +6 … or ×2)?
2. Ratio — is each term a fixed multiple of the previous one?
3. Squares/cubes — are terms near n² or n³ (± a small number)?
4. Alternation — two operations alternating, or two interleaved series?
5. Primes or special numbers.

If the numbers grow slowly, think differences; if they grow fast, think multiplication, squares, or cubes.

6. Common Traps Set by Examiners

• Near-correct options: If the answer is 37, options will include 36 and 38. Write your full calculation before looking at options.
• Double patterns: A series may look like +3, +5, +7 but actually be +prime numbers. Check one step further before deciding.
• Interleaved series disguised as one: If no single rule fits, split odd and even positions.
• Letter position slips: Confusing M (13) with N (14) is the most common error in alphabet series. Use EJOTY to verify.

7. Solved Examples

Q1. 11, 13, 17, 19, 23, ?
These are consecutive prime numbers. Next prime after 23 = 29.

Q2. 4, 18, 48, 100, ?
Try n³ + n²: 1+1=2? No. Try n² × (n+1): 1×2=2? No. Check n³ + n² for n=2: 8+4=12? No. Try differences: 14, 30, 52 — second differences 16, 22 — not clean. Try n²(n+1) starting n=1: 2, 12, 36, 100? No. Try n³ + n: 2, 10, 30, 68? No. Try (n+1)² × n… Instead note 4 = 2²×1, 18 = 3²×2, 48 = 4²×3, 100 = 5²×4 → next = 6²×5 = 180. (Lesson: when simple rules fail, compare each term with nearby squares.)

Q3. B, E, H, K, ?
Positions 2, 5, 8, 11 (+3) → 14 = N.

Q4. 3, 7, 16, 35, 74, ?
Check ×2 + 1: 3→7 ✓, 7→15 ✗. Check differences: 4, 9, 19, 39 — each is roughly double plus 1: 4×2+1=9, 9×2+1=19, 19×2+1=39 → next difference = 39×2+1 = 79 → answer = 74 + 79 = 153.

8. Key Takeaways

• Series = find the rule, apply the rule. No rule, no answer — never guess from "feel".
• Master squares to 25, cubes to 12, primes to 50, and letter positions (EJOTY).
• Use the fixed checking order: differences → ratio → squares/cubes → alternation → primes.
• For "wrong term" questions, the misfit breaks the difference pattern twice.
• Practise daily; speed in series comes from pattern memory, not calculation.

*Source: NCERT Class 6–10 Mathematics (patterns, squares, cubes, primes); PYQ-style reasoning practice.*