Introduction to Types of Number Series Questions in Bank Exams
Number series questions are a critical component of the reasoning or quantitative aptitude sections in bank exams such as IBPS PO, SBI PO, RBI Assistant, IBPS Clerk, and SBI Clerk. These questions assess a candidate’s ability to identify patterns in a sequence of numbers and determine the next number, missing number, or a specific term. They appear in both prelims (3-5 questions) and mains (5-8 questions), contributing significantly to sections worth 35-50 marks. Below is a detailed exploration of the various types of number series questions commonly encountered in bank exams, complete with examples and explanations to aid preparation.
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Number Series Questions – Practice Sets
»Find the Missing Number Reasoning SET 1
» 100 Wrong Number Series SET 1
» Find the Next Number in The Series SET 1
Types of Number Series Questions
Number series questions are categorized based on the underlying pattern or mathematical logic. The following are the primary types, each with distinct characteristics and illustrative examples:
1. Arithmetic Series
Description: Numbers follow a pattern where the difference between consecutive terms is constant (common difference). The series is based on addition or subtraction.
Formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.
Example: 3, 7, 11, 15, 19, ?
Pattern: Difference is 7-3 = 4, 11-7 = 4, etc. (common difference = 4).
Next term: 19 + 4 = 23.
Question: What is the next number? Answer: 23.
Bank Exam Context: Common in IBPS Clerk Prelims, SBI PO Prelims. May include negative differences or large numbers.
2. Geometric Series
Description: Numbers follow a pattern where each term is obtained by multiplying the previous term by a constant (common ratio).
Formula: a_n = a_1 · r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.
Example: 2, 6, 18, 54, 162, ?
Pattern: Ratio is 6/2 = 3, 18/6 = 3, etc. (common ratio = 3).
Next term: 162 · 3 = 486.
Question: What is the next number? Answer: 486.
Bank Exam Context: Seen in SBI PO Mains, IBPS PO Mains. May involve fractions or negative ratios in complex cases.
3. Square or Cube Series
Description: Numbers are squares (n^2) or cubes (n^3) of consecutive integers, sometimes with additional operations (e.g., +k, -k).
Example (Square Series): 1, 4, 9, 16, 25, ?
Pattern: 1^2, 2^2, 3^2, 4^2, 5^2 (squares of 1, 2, 3, 4, 5).
Next term: 6^2 = 36.
Question: What is the next number? Answer: 36.
Example (Cube Series): 8, 27, 64, 125, 216, ?
Pattern: 2^3, 3^3, 4^3, 5^3, 6^3 (cubes of 2, 3, 4, 5, 6).
Next term: 7^3 = 343.
Question: What is the next number? Answer: 343.
Bank Exam Context: Frequent in IBPS Clerk Mains, RBI Assistant Prelims. Variants may add/subtract constants (e.g., n^2 + 1).
4. Fibonacci-Based Series
Description: Each term is the sum of the two preceding terms, often with modifications (e.g., multiplied by a constant or offset).
Example: 1, 1, 2, 3, 5, 8, ?
Pattern: Fibonacci sequence (1+1=2, 1+2=3, 2+3=5, 3+5=8).
Next term: 5+8 = 13.
Question: What is the next number? Answer: 13.
Bank Exam Context: Appears in SBI PO Prelims, IBPS PO Mains. Modified versions (e.g., Fibonacci terms multiplied by 2) are common in mains.
5. Mixed Series (Combination of Operations)
Description: Combines multiple operations (addition, multiplication, squares, etc.) in a single series, requiring careful pattern identification.
Example: 2, 5, 11, 23, 47, ?
Pattern: Each term is obtained by previous term · 2 + 1 (e.g., 2 · 2 + 1 = 5, 5 · 2 + 1 = 11, 11 · 2 + 1 = 23, etc.).
Next term: 47 · 2 + 1 = 95.
Question: What is the next number? Answer: 95.
Bank Exam Context: Common in IBPS PO Mains, SBI PO Mains, RBI Assistant Mains. Tests advanced pattern recognition.
6. Alternating Series
Description: The series alternates between two or more patterns, often applying different operations to odd and even positions.
Example: 1, 4, 3, 16, 5, 64, ?
Pattern: Odd positions (1, 3, 5, …) increase by 2; even positions (4, 16, 64, …) are 2^2, 4^2, 8^2.
Next term (odd position): 5 + 2 = 7.
Question: What is the next number? Answer: 7.
Bank Exam Context: Seen in SBI Clerk Mains, IBPS Clerk Mains. Requires splitting the series into sub-sequences.
7. Difference-Based Series
Description: The differences between consecutive terms form a pattern (e.g., arithmetic, geometric, or constant).
Example: 2, 3, 6, 12, 22, ?
Differences: 3-2=1, 6-3=3, 12-6=6, 22-12=10.
Difference pattern: 1, 3, 6, 10 (increases by 2, 3, 4, …).
Next difference: 10 + 5 = 15.
Next term: 22 + 15 = 37.
Question: What is the next number? Answer: 37.
Bank Exam Context: Popular in IBPS PO Prelims, RBI Assistant Prelims. Differences may form complex patterns in mains.
8. Prime Number Series
Description: Numbers are based on prime numbers, either directly or with operations (e.g., prime + k, prime squares).
Example: 2, 3, 5, 7, 11, ?
Pattern: Prime numbers (2, 3, 5, 7, 11).
Next term: Next prime is 13.
Question: What is the next number? Answer: 13.
Bank Exam Context: Found in SBI PO Prelims, IBPS Clerk Prelims. Variants may involve prime multiples or offsets.
9. Factorial Series
Description: Terms are factorials (n!) or derived from factorials, sometimes with additional operations.
Example: 1, 2, 6, 24, 120, ?
Pattern: 1!, 2!, 3!, 4!, 5! (factorials).
Next term: 6! = 720.
Question: What is the next number? Answer: 720.
Bank Exam Context: Rare but appears in IBPS PO Mains, RBI Assistant Mains. Often combined with other operations.
10. Double or Triple Series
Description: The sequence is divided into two or three interleaved series, each following its own pattern.
Example: 1, 2, 4, 7, 8, 14, 16, ?
Pattern: Split into two series:
Odd positions: 1, 4, 8, 16 (multiply by 2: 1 · 2 = 2, 4 · 2 = 8, etc.).
Even positions: 2, 7, 14 (add 5, then 7: 2+5=7, 7+7=14).
Next term (even position): 14 + 9 = 23.
Question: What is the next number? Answer: 23.
Bank Exam Context: Common in SBI PO Mains, IBPS PO Mains. Requires identifying multiple patterns.
11. Missing Number Series
Description: A number in the series is missing, and candidates must identify it based on the pattern.
Example: 5, 10, 20, ?, 80, 160
Pattern: Each term is multiplied by 2 (5 · 2 = 10, 10 · 2 = 20, 20 · 2 = 40, etc.).
Missing term: 40.
Question: What is the missing number? Answer: 40.
Bank Exam Context: Frequent in IBPS Clerk Prelims, SBI Clerk Prelims. Tests pattern consistency.
12. Wrong Number Series
Description: One number in the series does not follow the pattern, and candidates must identify it.
Example: 2, 4, 8, 14, 32, 64
Pattern: Should be · 2 (i.e., 2, 4, 8, 16, 32, 64), but 14 breaks the pattern (should be 16).
Wrong term: 14.
Question: Which number is wrong? Answer: 14.
Bank Exam Context: Common in IBPS PO Mains, SBI PO Mains. Requires spotting deviations.
13. Exponential Series
Description: Numbers follow a pattern where terms are powers of a base, often with modifications.
Example: 2, 4, 16, 256, ?
Pattern: 2^1, 2^2, 2^4, 2^8 (exponents double: 1, 2, 4, 8).
Next term: 2^16 = 65536.
Question: What is the next number? Answer: 65536.
Bank Exam Context: Seen in RBI Assistant Mains, IBPS PO Mains. Tests exponential pattern recognition.
14. Pattern-Based Series with Operations on Differences
Description: The series involves operations on the differences between terms, which may form a secondary pattern.
Example: 1, 2, 6, 15, 31, ?
Differences: 2-1=1, 6-2=4, 15-6=9, 31-15=16 (squares: 1^2, 2^2, 3^2, 4^2).
Next difference: 5^2 = 25.
Next term: 31 + 25 = 56.
Question: What is the next number? Answer: 56.
Bank Exam Context: Appears in SBI PO Mains, IBPS Clerk Mains. Complex but common in higher-level exams.
15. Custom or Non-Standard Series
Description: Unique patterns not fitting standard categories, often involving creative combinations of operations.
Example: 1, 3, 12, 60, 360, ?
Pattern: 1 · 3 = 3, 3 · 4 = 12, 12 · 5 = 60, 60 · 6 = 360.
Next term: 360 · 7 = 2520.
Question: What is the next number? Answer: 2520.
Bank Exam Context: Rare but seen in IBPS PO Mains, RBI Assistant Mains. Tests innovative thinking.
Key Features of Number Series Questions in Bank Exams
Difficulty Levels:
Prelims: Simple arithmetic, geometric, or square series (e.g., Q1-5 in IBPS Clerk Prelims).
Mains: Complex mixed, alternating, or wrong number series (e.g., Q12 in SBI PO Mains).
Formats:
Next Number: Find the next term (most common).
Missing Number: Identify a missing term in the sequence.
Wrong Number: Spot the term that breaks the pattern.
Time Sensitivity: Questions require quick pattern recognition, as candidates have ~1 minute per question in prelims.
Scoring: High accuracy can boost reasoning/aptitude scores, as these questions are objective and less prone to errors if patterns are mastered.
Tips for Solving Number Series Questions
1. Check for Common Patterns First: Look for arithmetic (constant difference), geometric (constant ratio), or square/cube patterns.
2. Calculate Differences: Find differences between terms to identify secondary patterns (e.g., differences forming squares).
3. Split the Series: For alternating or double series, separate odd and even positions.
4. Test Operations: Try multiplication, division, or combined operations if simple addition/subtraction fails.
5. Look for Anomalies: In wrong number questions, compare each term to the expected pattern.
6. Practice Variations: Familiarize yourself with mixed and non-standard series for mains exams.
7. Use Elimination: In MCQs, eliminate unlikely options based on the series’ trend.
Sample Bank Exam Questions
1. [IBPS PO Prelims 2020] What is the next number in the series: 4, 12, 36, 108, ?
Pattern: Geometric, each term is multiplied by 3 (4 · 3 = 12, 12 · 3 = 36, etc.).
Next term: 108 · 3 = 324.
Answer: 324.
2. [SBI Clerk Mains 2021] Which number is wrong in the series: 3, 5, 10, 18, 30, 45?
Pattern: Differences should be 2, 5, 8, 11, 14 (increase by 3), but 18-10=8, 30-18=12 (12 is wrong, should be 11).
Wrong term: 30 (should be 29).
Answer: 30.
3. [RBI Assistant Mains 2022] Find the missing number: 7, 14, ?, 84, 336, 1008.
Pattern: Multiply by 2, 3, 4, … (7 · 2 = 14, 14 · 3 = 42, 42 · 4 = 168, etc.).
Missing term: 42.
Answer: 42.
Conclusion
Number series questions in bank exams test a range of mathematical and logical skills through patterns like arithmetic, geometric, Fibonacci, mixed, and wrong number series.
Understanding these types—arithmetic, geometric, square/cube, Fibonacci, mixed, alternating, difference-based, prime, factorial, double/triple, missing, wrong, exponential, and custom—equips candidates to tackle both prelims and mains effectively.
Regular practice with varied patterns, quick calculation skills, and familiarity with exam-specific formats (e.g., IBPS PO vs. SBI Mains) are key to mastering this topic. For further preparation, candidates can practice with mock tests or previous year papers from sources like .
