Sequence and Series - Reasoning Notes
Introduction
In logical reasoning, Sequence and Series questions are
designed to test a candidate’s ability to identify patterns in a list of
numbers, letters, or a combination of both. These questions are common in exams
like CUET, CLAT, and IPMAT because they assess analytical thinking, attention
to detail, and the ability to recognize logical order.
Key Concepts
1. Sequence
A sequence is an ordered list of numbers, alphabets, or a
combination, where each item follows a specific rule or pattern.
2. Series
A series is a sequence where terms are often summed or
connected logically, and the missing or next term must be found.
3. Common Types
- Number
series
- Alphabet
series
- Alpha-numeric
series
- Mixed
series
- Logical
pattern-based series
Number Series
Types of Number Series
- Arithmetic
Series (AP): Constant difference between consecutive terms.
- Example:
3, 6, 9, 12, ...
- Geometric
Series (GP): Constant ratio between consecutive terms.
- Example:
2, 4, 8, 16, ...
- Squares/Cubes
Series: Based on perfect squares or cubes.
- Example:
1, 4, 9, 16, 25, ...
- Prime
Number Series: Based on prime numbers.
- Example:
2, 3, 5, 7, 11, ...
- Fibonacci
Series: Each term is the sum of the previous two terms.
- Example:
0, 1, 1, 2, 3, 5, 8, ...
- Difference
Pattern: Changing differences or multiple difference layers.
- Example:
1, 2, 4, 7, 11, 16, ...
Examples and Solutions
Example 1:
Find the next number in the series:
5, 11, 17, 23, ?
Solution:
The difference between terms is constant:
11 - 5 = 6
17 - 11 = 6
23 - 17 = 6
So, next number = 23 + 6 = 29
Example 2:
Find the missing number:
2, 4, 8, 16, ?, 64
Solution:
It's a geometric series (×2):
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
32 × 2 = 64
Answer: 32
Example 3:
What comes next?
1, 4, 9, 16, 25, ?
Solution:
Perfect squares:
1², 2², 3², 4², 5², next is 6² = 36
Answer: 36
Example 4:
Find the missing term:
2, 3, 5, 7, 11, ?
Solution:
Prime number series:
Next prime after 11 is 13
Alphabet Series
Patterns
- Consecutive
Letters
- Example:
A, B, C, D, ...
- Skipping
Letters
- Example:
A, C, E, G, ...
- Reverse
Order
- Example:
Z, Y, X, ...
- Letter
Positions (A=1, B=2, ..., Z=26)
Examples and Solutions
Example 1:
Find the next letter:
A, D, G, J, ?
Solution:
Positions: A(1), D(4), G(7), J(10) → +3 each time
Next = 10 + 3 = 13 → M
Answer: M
Example 2:
Find the missing letter:
Z, X, V, T, ?
Solution:
Positions: Z(26), X(24), V(22), T(20) → -2 each time
Next = 20 - 2 = 18 → R
Answer: R
Example 3:
Find the next term:
AZ, BY, CX, ?
Solution:
Pattern:
- First
letters: A, B, C → D
- Second
letters: Z, Y, X → W
Answer: DW
Alpha-Numeric Series
These combine letters and numbers, often in repeated logical
patterns.
Example:
A1, C3, E5, G7, ?
Solution:
- Letters:
A, C, E, G → skipping 1 letter → next: I
- Numbers:
1, 3, 5, 7 → odd numbers → next: 9
Answer: I9
Mixed Series (Symbols, Numbers, Letters)
Involves patterns of symbols, letters, and numbers arranged
in sequences.
Example:
2B, 4D, 6F, 8H, ?
Solution:
- Numbers:
2, 4, 6, 8 → +2 → next = 10
- Letters:
B(2), D(4), F(6), H(8) → even positions → next: J(10)
Answer: 10J
Logical Pattern-Based Series
These require observing patterns not directly numerical or
alphabetical—may involve reverse orders, interchanging positions, or complex
patterns.
Examples and Solutions
Example 1:
Find the missing number:
121, 144, 169, ?, 225
Solution:
All are squares:
- 121 =
11²
- 144 =
12²
- 169 =
13²
- ? =
14² = 196
- 225 =
15²
Answer: 196
Example 2:
Find the next number:
3, 6, 11, 18, 27, ?
Solution:
Differences:
6-3 = 3
11-6 = 5
18-11 = 7
27-18 = 9
Next difference = 11
So next term = 27 + 11 = 38
Example 3:
Find the missing term:
A1, B3, D5, G7, ?
Solution:
Letters: A → B (+1), B → D (+2), D → G (+3) → Next +4 = K
Numbers: 1, 3, 5, 7 → +2 → next = 9
Answer: K9
Strategies to Solve
- Look
at differences: Use first and second-level differences.
- Check
for arithmetic/geometric rules
- Observe
square, cube, or prime patterns
- Convert
letters to positions (A=1 to Z=26)
- Use
options (if MCQ) to back-solve
- Write
down each step for clarity
- Identify
combinations (if multiple elements)
Practice Questions
Q1: Find the next number:
7, 14, 28, 56, ?
Solution:
×2 pattern → 56 × 2 = 112
Q2: Find the missing term:
C, F, I, L, ?
Solution:
Letters increase by 3 in position:
C(3) → F(6) → I(9) → L(12) → O(15)
Answer: O
Q3: What is the next term?
Z1, X2, V3, T4, ?
Solution:
Letters: Z, X, V, T → -2 each time → R
Numbers: 1, 2, 3, 4 → +1 → 5
Answer: R5
Q4: Find the next term:
1, 4, 10, 22, 46, ?
Solution:
Differences:
4-1 = 3
10-4 = 6
22-10 = 12
46-22 = 24
Next difference = 48
So, next term = 46 + 48 = 94
🔢 CUET Previous Year
Questions (8 Questions)
Q1. Find the next number in the series:
7, 10, 16, 25, 37, ?
Solution:
+3, +6, +9, +12, +15 → next: +18 → 55
Q2. What comes next:
2, 6, 12, 20, 30, ?
Solution:
Differences: 4, 6, 8, 10, → next: 12
So, 30 + 12 = 42
Q3. Find the missing term:
A, C, F, J, O, ?
Solution:
Positions: A(1), C(3), F(6), J(10), O(15) → +2, +3, +4, +5 → next: +6 → 21 → U
Q4. What comes next:
AZ, BY, CX, ?
Solution:
A-Z, B-Y, C-X → letters are moving opposite ways in the alphabet.
Next: D-W
Q5. Find the missing term:
1, 2, 6, 24, ?, 720
Solution:
Factorial pattern:
1, 2, 3!, 4!, ? = 5! = 120
Q6. Find the next term:
13, 17, 19, 23, 29, ?
Solution:
Prime numbers → next prime after 29 is 31
Q7. Choose the correct term:
1, 3, 7, 15, ?, 63
Solution:
Pattern: ×2 +1
1×2+1 = 3
3×2+1 = 7
7×2+1 = 15
15×2+1 = 31
31×2+1 = 63
Answer: 31
Q8. What comes next:
Z, X, V, T, ?
Solution:
-2 each time → R
⚖️ CLAT Previous Year Questions
(6 Questions)
Q9. What comes next:
3, 6, 18, 72, ?
Solution:
×2, ×3, ×4, ... → next ×5 = 360
Answer: 360
Q10. Find the next term:
100, 97, 91, 82, ?
Solution:
-3, -6, -9, -12 → next: -15 → 82 - 15 = 67
Q11. Identify the missing term:
A2, C4, E6, G8, ?
Solution:
+2 in letters and numbers → next: I10
Q12. What comes next:
21, 25, 33, 49, ?
Solution:
+4, +8, +16 → next +32 → 49 + 32 = 81
Q13. What is the missing term:
2, 3, 5, 8, 12, 17, ?
Solution:
+1, +2, +3, +4, +5 → next: +6 → 23
Q14. What comes next:
AB, CD, EF, GH, ?
Solution:
Consecutive letters → next: IJ
📘 IPMAT Previous Year
Questions (6 Questions)
Q15. Find the missing number:
5, 9, 17, 33, ?
Solution:
+4, +8, +16 → next: +32 → 33 + 32 = 65
Q16. What comes next:
A1, B2, C3, D4, ?
Solution:
Letter + number increasing → next: E5
Q17. Choose the missing term:
1, 4, 9, 16, ?, 36
Solution:
Perfect squares → 1², 2², 3², 4², ? = 5² = 25
Q18. What comes next:
5, 10, 20, 40, ?
Solution:
×2 each time → next: 80
Q19. Identify the next term:
1, 5, 14, 30, 55, ?
Solution:
Differences: 4, 9, 16, 25 → squares → next: +36 → 91
Q20. What comes next:
M, N, P, S, ?
Solution:
Positions: M(13), N(14), P(16), S(19) → +1, +2, +3 → next +4 = 23 → W
Important Tips
- Memorize
letter positions in the alphabet.
- Be
familiar with squares, cubes, and prime numbers.
- Use
elimination method in MCQs.
- Don’t
overthink simple patterns.
- Practice
mixed and tricky patterns for exams like IPMAT.
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