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Series Completion

Practice MCQs

None

Reasoning Ability Series Completion Competitive Exams

Series Completion questions test your ability to identify a pattern in a given series and find the missing or next term. The series may contain numbers, alphabets, letters, symbols, or a combination of these.

What is Series Completion?

In Series Completion, a sequence of terms is given. Each term follows a certain rule or pattern. You have to identify that rule and find the missing term or the next term.

The pattern may be based on addition, subtraction, multiplication, division, squares, cubes, alternate terms, alphabet positions, reverse order, or mixed logic.

Quick idea: First compare consecutive terms. If the difference is not fixed, check multiplication, squares, cubes, alternating patterns, or alphabet positions.
Series Type Pattern Used Example
Number Series Addition, subtraction, multiplication, division 2, 4, 6, 8, ?
Alphabet Series Alphabet positions and letter gaps A, C, E, G, ?
Alphanumeric Series Combination of letters and numbers A1, B2, C3, ?
Alternate Series Odd and even positions follow different patterns 2, 10, 4, 20, 6, ?
Mixed Series More than one rule is used 3, 6, 12, 24, ?

“Series questions become easy when the hidden gap between terms is identified.”

Reasoning Tip
Key Points
  • Compare consecutive terms first.
  • Check whether the gap is constant.
  • Look for increasing or decreasing differences.
  • Check alternate terms separately.
  • Use alphabet positions for letter series.
  • Do not assume only one type of pattern.
numbers alphabets patterns logic

Common Series Patterns

Most series completion questions are based on one of the following common patterns.

1. Addition Series

A fixed number is added each time.

5, 10, 15, 20, ?
Add 5 each time.
Answer = 25
2. Subtraction Series

A fixed number is subtracted each time.

50, 45, 40, 35, ?
Subtract 5 each time.
Answer = 30
3. Multiplication Series

Each term is multiplied by a fixed number.

3, 6, 12, 24, ?
Multiply by 2.
Answer = 48
4. Square Series

Terms are squares of natural numbers.

1, 4, 9, 16, ?
\(1^2, 2^2, 3^2, 4^2\)
Answer = 25
Tip: If direct difference does not work, check square, cube, multiplication, division, and alternate-position patterns.

Important Number Series Patterns

Pattern Rule Example Answer
Constant Addition Add same number 7, 14, 21, 28, ? 35
Constant Subtraction Subtract same number 90, 80, 70, 60, ? 50
Increasing Difference Add increasing numbers 2, 5, 9, 14, ? 20
Multiplication Multiply by same number 4, 8, 16, 32, ? 64
Squares Square of numbers 1, 4, 9, 16, ? 25
Cubes Cube of numbers 1, 8, 27, 64, ? 125
Alternate Terms Odd and even positions differ 2, 10, 4, 20, 6, ? 30
Important: In alternate series, check terms in odd positions separately and terms in even positions separately.

Alphabet Series Patterns

In alphabet series, letters are usually arranged according to their alphabet positions. Use A = 1, B = 2, C = 3, and so on.

ABCDEFGHIJKLM
12345678910111213
NOPQRSTUVWXYZ
14151617181920212223242526
Example: A, C, E, G, ?
Positions: 1, 3, 5, 7
Next position = 9
Answer = I
Example: Z, X, V, T, ?
Positions: 26, 24, 22, 20
Next position = 18
Answer = R

Step-by-Step Solving Method

Step Action Example
Step 1 Identify the type of series. Number, alphabet, mixed, or alternate
Step 2 Compare consecutive terms. 2, 5, 9, 14
Step 3 Find the difference or relation. +3, +4, +5
Step 4 Apply the same pattern to the next term. Next difference = +6
Step 5 Verify the answer with the full series. 14 + 6 = 20
Important: If one pattern fails, do not force it. Try another pattern such as alternate terms, multiplication, square, cube, or letter positions.

Worked Example 1: Increasing Difference

Find the next term: 2, 5, 9, 14, ?

Terms 2 5 9 14 ?
Difference +3 +4 +5 +6
The next difference is \(+6\). So, \(14 + 6 = 20\).
Answer = 20.

Worked Example 2: Alphabet Series

Find the next term: B, D, G, K, ?

Letter B D G K ?
Position 2 4 7 11 16
Difference +2 +3 +4 +5
Position 16 corresponds to P.
Answer = P.

Worked Example 3: Alternate Series

Find the missing term: 2, 10, 4, 20, 6, ?

Odd position terms: 2, 4, 6 → increase by 2.
Even position terms: 10, 20, ? → increase by 10.
Therefore, the next even-position term is \(20 + 10 = 30\).
Answer = 30.

Common Types of Series Completion Questions

Number Series

Based on arithmetic or numeric patterns.

  • Addition
  • Subtraction
  • Multiplication
  • Squares and cubes
Alphabet Series

Based on letter positions.

  • Forward gap
  • Backward gap
  • Alternate letters
  • Reverse alphabet
Mixed Series

Uses more than one type of logic.

  • Letters and numbers
  • Symbols and digits
  • Alternating terms
  • Combined patterns
Missing Term

Find a term in the middle or end.

  • Next term
  • Middle missing term
  • Wrong term
  • Final term
Rule: In series completion, the correct answer must fit the complete pattern, not just the last two terms.

Solved Examples

Question Pattern Answer
5, 10, 15, 20, ? Add 5 each time 25
60, 55, 50, 45, ? Subtract 5 each time 40
3, 6, 12, 24, ? Multiply by 2 48
1, 4, 9, 16, ? Squares: \(1^2, 2^2, 3^2, 4^2\) 25
1, 8, 27, 64, ? Cubes: \(1^3, 2^3, 3^3, 4^3\) 125
A, C, E, G, ? Skip one letter each time I
Z, X, V, T, ? Move backward by 2 letters R
2, 10, 4, 20, 6, ? Alternate series: even terms 10, 20, 30 30

Note: If the series contains both letters and numbers, solve letter pattern and number pattern separately.

Common Traps and Shortcuts

Common Traps
  • Checking only the last two terms.
  • Ignoring alternate-position patterns.
  • Confusing square series with multiplication series.
  • Forgetting alphabet positions.
  • Forcing one pattern even when it does not fit all terms.
  • Missing increasing or decreasing differences.
Useful Shortcuts
  • Check differences first.
  • Check second-level differences if needed.
  • Try multiplication and division patterns.
  • Check squares and cubes quickly.
  • Separate odd and even positions.
  • Convert alphabets to numbers when needed.
Exam approach: Identify whether the series is based on addition, subtraction, multiplication, squares, cubes, alphabet positions, or alternate terms.

Practice

A) Multiple Choice Questions
  1. Find the next term: 6, 12, 18, 24, ?
    28 30 32 36
  2. Find the next term: 100, 90, 80, 70, ?
    50 55 60 65
  3. Find the next term: 2, 4, 8, 16, ?
    24 28 32 36
  4. Find the next term: A, D, G, J, ?
    K L M N
  5. Find the missing term: 3, 15, 6, 30, 9, ?
    35 40 45 50
B) Solve the Higher-Order Problems
  1. Find the next term: 4, 9, 15, 22, ? Hint: Check increasing differences.
  2. Find the next term: 1, 4, 9, 16, 25, ? Hint: These are square numbers.
  3. Find the next term: C, F, J, O, ? Hint: Convert letters to alphabet positions.
  4. Find the missing term: 5, 25, 10, 50, 15, ? Hint: Check odd and even positions separately.
  5. Find the next term: 2, 6, 12, 20, 30, ? Hint: Differences are increasing even numbers.
Reasoning Reminder

Series completion questions require pattern recognition. Start with simple differences, then try multiplication, squares, cubes, alphabet positions, or alternate-term logic.

Task: Create five series questions using addition, multiplication, squares, alphabet gaps, and alternate terms.

Show Suggested Answers
Multiple Choice
  1. 30
    Pattern: Add 6 each time. \(24 + 6 = 30\).
  2. 60
    Pattern: Subtract 10 each time. \(70 - 10 = 60\).
  3. 32
    Pattern: Multiply by 2. \(16 \times 2 = 32\).
  4. M
    A, D, G, J have positions 1, 4, 7, 10. Add 3 each time. Next position = 13 = M.
  5. 45
    Odd terms: 3, 6, 9. Even terms: 15, 30, 45. Answer = 45.
Higher-Order Problems
  1. 4, 9, 15, 22, ?
    Differences: +5, +6, +7. Next difference = +8.
    \(22 + 8 = 30\).
    Answer = 30.
  2. 1, 4, 9, 16, 25, ?
    These are \(1^2, 2^2, 3^2, 4^2, 5^2\).
    Next = \(6^2 = 36\).
    Answer = 36.
  3. C, F, J, O, ?
    Positions: 3, 6, 10, 15.
    Differences: +3, +4, +5. Next difference = +6.
    Next position = 21 = U.
    Answer = U.
  4. 5, 25, 10, 50, 15, ?
    Odd terms: 5, 10, 15. Even terms: 25, 50, 75.
    Answer = 75.
  5. 2, 6, 12, 20, 30, ?
    Differences: +4, +6, +8, +10. Next difference = +12.
    \(30 + 12 = 42\).
    Answer = 42.
Clue Explanation

In series completion, the answer must follow the same rule throughout the series. If direct differences do not work, check alternate terms, squares, cubes, or alphabet positions.

Exam Tips
  • Find differences between terms first.
  • Check second-level differences if needed.
  • Try multiplication or division patterns.
  • Check squares and cubes quickly.
  • For alphabet series, write letter positions.
  • Check odd and even terms separately in mixed series.
Practice MCQs