CAT Logical Sequence : Basic Concepts and Notes PDF

What is Logical Sequence

Logical sequence questions require identifying a rule or pattern that governs a series of letters, numbers or symbols, and then using that rule to predict the next item or fill a missing element. Such questions test observation, pattern recognition and simple reasoning.

Example:

Series: 2, 5, 10, 17, ---, 37

Calculate differences between consecutive terms to find the rule:
5 - 2 = 3
10 - 5 = 5
17 - 10 = 7

The successive differences are 3, 5, 7 - consecutive odd numbers increasing by 2. Continue the pattern:

Next difference = 9
17 + 9 = 26

Therefore the missing term is 26, and the complete series is 2, 5, 10, 17, 26, 37.

Types of Logical Sequence Questions

 Logical sequences can be broadly categorized into two types: alphabet-based sequences and number-based sequences.

• Alphabet-based sequences: The rule uses positions of letters in the alphabet. Common patterns are fixed skips (every 2nd, 3rd letter), alternating directions, or simultaneous independent changes in multiple letter positions (for example, first letter moves forward while last letter moves backward).

  Example: A, C, E, G, ---, K

  Here letters advance by two positions each time (A→C→E→G→I→K). The missing letter is I. Full sequence: A, C, E, G, I, K.

• Number-based sequences: The rule uses arithmetic or multiplicative relationships (addition/subtraction of a fixed number, multiplication/division, alternating operations, squares/cubes, factorials, recursive relations, etc.). Recognise whether a single operation or more complex recurrence is in use.

  Example: 2, 4, 8, 16, ---, 64

  Each term is double the previous one (×2). The missing term is 32. Full sequence: 2, 4, 8, 16, 32, 64.

Understanding the distinction between these two types of sequences is crucial when solving logical sequence questions. It requires keen observation and an analytical mindset to identify the underlying pattern correctly. Whether it's identifying letter patterns or numerical relationships, these types of questions assess one's ability to recognize and apply logical rules in a systematic manner.

Tips and Tricks

• Practice regularly to become familiar with common patterns (AP, GP, alternate sequences, factorial-based, powers, digit manipulations).
• Identify the type quickly - decide if the sequence is alphabetic or numeric, and whether operations look additive, multiplicative, or recursive.
• Start simple - first check for arithmetic progression, geometric progression, simple alternation, or repeated fixed blocks.
• Consider alternate or interleaved patterns - sometimes two independent sequences are interleaved (odd and even positions follow different rules).
• Use options strategically - in multiple-choice questions, substitute each option into the sequence to test which fits the pattern.
• Check endpoints - first and last terms can offer clues; sometimes the rule applies differently at ends (e.g., wrap-around alphabet).
• Elimination technique - discard options that clearly violate the observed pattern to improve chances if unsure.

Remember, with regular practice and exposure to different types of sequences, you'll develop a sharper intuition for recognizing patterns, making it easier to tackle these questions efficiently in competitive exams.

Solved Examples

Question 1

Find the missing letters in the pattern:

E_G_EFF_E_FG_FG_EF
 (a) GFGEEE
 (b) FGGGEF
 (c) FGGEEG
 (d) EGFEFG

Correct Answer is Option (c)

Explanation: The sequence is built from the three letters E, F and G repeating in a structured way. The series follows, +1,+1,+0 addition pattern. On inspection, inserting option (c) into the blanks yields a consistent repetition of short patterns and restores the frequency and adjacency of E, F and G as observed elsewhere in the series. Among the given choices, option (c) is the only one that completes the sequence without creating an abnormal adjacency or an unmatched count of letters, therefore it is correct.

Question 2

Find the missing letters in the pattern:

_CAM_AMC_M_A_CAM
 (a) CMAMC
 (b) MACAM
 (c) MCAMC
 (d) MCACM

Correct Answer is Option (d)

Explanation: The visible parts show repetition of the block MCA. Filling blanks with the letters of this repeated block gives a continuous pattern: MCA MCA MCA MCA MCA. Option (d) MCACM provides the letters that, when placed into the blanks, maintain the repeating MCA blocks throughout the series.

Question 3

2, 3, 8, 27, 112, ?
 (a) 156
 (b) 224
 (c) 375
 (d) 565

Correct Answer is Option (d)

Explanation: The sequence follows a recursive rule where each term is obtained from the previous term by multiplying by the index (starting with 1) and then adding the same index.

Write terms with their indices starting from 1:
a1 = 2

a2 = a1 × 1 + 1 = 2 × 1 + 1 = 3
a3 = a2 × 2 + 2 = 3 × 2 + 2 = 8
a4 = a3 × 3 + 3 = 8 × 3 + 3 = 27
a5 = a4 × 4 + 4 = 27 × 4 + 4 = 112

Apply the same rule to get the next term:
a6 = a5 × 5 + 5 = 112 × 5 + 5 = 560 + 5 = 565

Hence the correct option is 565 (option d).

Question 4

What will be the next term in? 
 ZAM, YBL, ----, WDJ, VEI
 (a) XCK
 (b) UFH
 (c) ZAC
 (b) PFD

Correct Answer is Option (a)

Explanation: Examine the three-letter groups column-wise.

First letters: Z, Y, X, W, V - they decrease by one letter each time.
Second letters: A, B, C, D, E - they increase by one letter each time.
Third letters: M, L, K, J, I - they decrease by one letter each time.

Combining the three-letter letters for the missing middle term gives X C K, which matches option (a) XCK.

Question 5

G, T, I, R, K, P, ___,___
 (a) M,N
 (b) O,P
 (c) Q,R
 (d) S,T

Correct Answer is Option (a)

Explanation: Convert letters to their alphabet positions:

G = 7, T = 20, I = 9, R = 18, K = 11, P = 16

Observe two interleaved sequences:

Positions at odd places: 7, 9, 11 → increase by 2 each time. Next odd-position term = 13 → letter M.

Positions at even places: 20, 18, 16 → decrease by 2 each time. Next even-position term = 14 → letter N.

Therefore the next two letters are M, N (option a).

Question 6

Find the wrong number in the given series?

3, 6, 11, 18, 29, 38, 51, 66
 (a) 18
 (b) 29
 (c) 38
 (d) 51

Correct Answer is Option (b)

Explanation: The pattern is formed by adding consecutive odd numbers starting from 3.

3 + 3 = 6
6 + 5 = 11
11 + 7 = 18
18 + 9 = 27 (but the sequence shows 29 here - mismatch)
27 + 11 = 38
38 + 13 = 51
51 + 15 = 66

Since 29 appears where 27 is expected, 29 is the wrong term (option b).

Question 7

Find the wrong number in the given series?

9, 28, 65, 126, 217, 344, 213
 (a) 65
 (b) 126
 (c) 217
 (d) 213

Correct Answer is Option (d)

Explanation: Recognise the pattern n³ + 1 starting with n = 2:

2³ + 1 = 8 + 1 = 9
3³ + 1 = 27 + 1 = 28
4³ + 1 = 64 + 1 = 65
5³ + 1 = 125 + 1 = 126
6³ + 1 = 216 + 1 = 217
7³ + 1 = 343 + 1 = 344
8³ + 1 = 512 + 1 = 513 (expected next)

The term 213 is incorrect because it breaks the increasing n³ + 1 pattern; hence option (d) is the wrong term.

Question 8

Arrange the words given below in a meaningful sequence.

1. Rainbow   2. Rain   3. Sun   4. Happy   5. Child

(a)   4, 2, 3, 5, 1

(b)   2, 3, 1, 5, 4

(c)   4, 5, 1, 2, 3

(d)   2, 1, 4, 5, 3

Correct Answer is Option (b)

Explanation: A logical event order is:

Rain (2) → Sun (3) → Rainbow (1) → Child (5) → Happy (4)

The natural sequence is rain followed by sun (sunlight + rain creates a rainbow), a child seeing the rainbow becomes happy. That corresponds to 2, 3, 1, 5, 4 (option b).

Question 9

Arrange the words given below in a meaningful sequence.

1. Probation   2. Interview   3. Selection
 4. Appointment   5. Advertisement   6. Application

(a)   5, 6, 3, 2, 4, 1

(b)   5, 6, 4, 2, 3, 1

(c)   5, 6, 2, 3, 4, 1

(d)   6, 5, 4, 2, 3, 1

Correct Answer is Option (c)

Explanation: The normal recruitment process is:

Advertisement (5) → Application (6) → Interview (2) → Selection (3) → Appointment (4) → Probation (1)

Thus the meaningful order is 5, 6, 2, 3, 4, 1 which is option (c).

Question 10

Find the missing series.

G2X, J4V, M8T, ?, S32P

(a) N64S 
(b) P16R  
(c) Q16R 
(d) P8S

Correct Answer is Option (b)

Explanation: Examine each of the three positions separately.

First letters: G (7), J (10), M (13), P (16), S (19) - increase by 3 each time.
Numbers: 2, 4, 8, 16, 32 - each term is double the previous (×2).
Last letters: X (24), V (22), T (20), R (18), P (16) - decrease by 2 each time.

Therefore the fourth element must be P16R, which is option (b).