Series Completion: Master Number & Alphabet Sequences Fast

102 views Ch 02: Series

📖 Introduction

Series Completion is a fundamental chapter in Verbal Reasoning that tests your ability to identify patterns and logical sequences. In these questions, you are given a series with one or more missing terms, and you must find the missing element(s) based on the pattern.

🔤 Types of Series

Series Type	Description	Example
Letter Series	Sequences of alphabets following a pattern	A, C, E, G, ?
Number Series	Sequences of numbers following a pattern	2, 4, 8, 16, ?
Alpha-Numeric Series	Combination of letters and numbers	A1, B2, C3, ?
Mixed/Pattern Series	Complex patterns with symbols or mixed elements	@A1, #B2, $C3, ?

📝 Letter Series

Understanding Letter Positions

First, memorize the position of each letter:

Letter	Position	Letter	Position	Letter	Position
A	1	J	10	S	19
B	2	K	11	T	20
C	3	L	12	U	21
D	4	M	13	V	22
E	5	N	14	W	23
F	6	O	15	X	24
G	7	P	16	Y	25
H	8	Q	17	Z	26
I	9	R	18

Quick Memory Trick: EJOTY Formula

Letter	E	J	O	T	Y
Position	5	10	15	20	25

Tip: Remember "EJOTY" - each letter is at a multiple of 5!

Type 1: Simple Letter Series

Pattern: Letters follow a consistent gap.

Example 1:

Series: A, C, E, G, ?

Position	1st	2nd	3rd	4th	5th
Letter	A	C	E	G	?
Position Number	1	3	5	7	9
Gap	—	+2	+2	+2	+2

Answer: I (Position 9)

Example 2:

Series: Z, W, T, Q, ?

Position	1st	2nd	3rd	4th	5th
Letter	Z	W	T	Q	?
Position Number	26	23	20	17	14
Gap	—	-3	-3	-3	-3

Answer: N (Position 14)

Type 2: Alternating Letter Series

Pattern: Two or more series running parallel.

Example 3:

Series: A, Z, B, Y, C, X, D, ?

Odd Positions	A	B	C	D	—
Pattern	+1	+1	+1	—	—

Even Positions	Z	Y	X	?	—
Pattern	-1	-1	-1	—	—

Answer: W

Type 3: Letter Group Series

Pattern: Groups of letters follow a pattern.

Example 4:

Series: ABC, BCD, CDE, ?

Group	1st	2nd	3rd	4th
Letters	ABC	BCD	CDE	DEF
Pattern	Each group shifts by +1 position

Answer: DEF

Example 5:

Series: AZ, BY, CX, ?

Group	1st Letter	2nd Letter
AZ	A (1)	Z (26)
BY	B (2)	Y (25)
CX	C (3)	X (24)
?	D (4)	W (23)

Pattern: First letter: +1, Second letter: -1

Answer: DW

Type 4: Missing Letter Series (Pattern Completion)

Example 6:

Series: a_bc_a_bcaa_caa_c

Step-by-Step Solution:

Step	Action
1	Identify the repeating unit
2	The pattern appears to be: aabc
3	Fill in the blanks

Complete Series: aabcaabcaabcaabc

Answer: aabbc

🔢 Number Series

Common Number Series Patterns

Pattern Type	Description	Example
Arithmetic	Constant difference	2, 5, 8, 11, 14 (+3)
Geometric	Constant ratio	2, 6, 18, 54 (×3)
Square	Perfect squares	1, 4, 9, 16, 25
Cube	Perfect cubes	1, 8, 27, 64, 125
Fibonacci	Sum of previous two	1, 1, 2, 3, 5, 8, 13
Prime	Prime numbers	2, 3, 5, 7, 11, 13
Triangular	n(n+1)/2	1, 3, 6, 10, 15

Type 1: Arithmetic Series

Example 7:

Series: 5, 11, 17, 23, ?

Term	1st	2nd	3rd	4th	5th
Value	5	11	17	23	?
Difference	—	+6	+6	+6	+6

Answer: 29

Type 2: Geometric Series

Example 8:

Series: 3, 12, 48, 192, ?

Term	1st	2nd	3rd	4th	5th
Value	3	12	48	192	?
Ratio	—	×4	×4	×4	×4

Answer: 768

Type 3: Square Series

Example 9:

Series: 1, 4, 9, 16, 25, ?

Term	1st	2nd	3rd	4th	5th	6th
Value	1	4	9	16	25	?
Pattern	1²	2²	3²	4²	5²	6²

Answer: 36

Type 4: Difference of Differences (Second Order)

Example 10:

Series: 2, 5, 10, 17, 26, ?

Term	1st	2nd	3rd	4th	5th	6th
Value	2	5	10	17	26	?
1st Difference	—	3	5	7	9	11
2nd Difference	—	—	2	2	2	2

Answer: 26 + 11 = 37

Type 5: Mixed Operations

Example 11:

Series: 2, 3, 5, 8, 13, 21, ?

Term	1st	2nd	3rd	4th	5th	6th	7th
Value	2	3	5	8	13	21	?

Pattern: Each term = Sum of previous two terms (Fibonacci-like)

Answer: 13 + 21 = 34

Type 6: Alternating Operations

Example 12:

Series: 2, 4, 12, 14, 42, 44, ?

Position	1st	2nd	3rd	4th	5th	6th	7th
Value	2	4	12	14	42	44	?
Operation	—	+2	×3	+2	×3	+2	×3

Answer: 44 × 3 = 132

Type 7: Complex Pattern Series

Example 13:

Series: 1, 2, 6, 24, 120, ?

Term	Value	Pattern
1st	1	1! = 1
2nd	2	2! = 2
3rd	6	3! = 6
4th	24	4! = 24
5th	120	5! = 120
6th	?	6! = 720

Answer: 720 (Factorial Series)

🔣 Alpha-Numeric Series

Type 1: Simple Alpha-Numeric

Example 14:

Series: A1, B2, C3, D4, ?

Position	Letter	Number
1st	A	1
2nd	B	2
3rd	C	3
4th	D	4
5th	E	5

Pattern: Letter +1, Number +1

Answer: E5

Type 2: Complex Alpha-Numeric

Example 15:

Series: A2, C6, E12, G20, ?

Term	Letter	Number	Letter Pattern	Number Pattern
1st	A (1)	2	—	1×2
2nd	C (3)	6	+2	2×3
3rd	E (5)	12	+2	3×4
4th	G (7)	20	+2	4×5
5th	I (9)	30	+2	5×6

Answer: I30

💡 Tips and Tricks

Quick Strategy Guide

Step	Action	Purpose
1	Observe	Look at the series carefully
2	Calculate Differences	Find gaps between consecutive terms
3	Check Ratios	If differences vary, check multiplication
4	Look for Patterns	Squares, cubes, primes, factorials
5	Check Alternating	Two series might be interleaved
6	Verify	Confirm pattern works for all terms

Common Patterns Cheat Sheet

If You See	Think About
Large jumps	Multiplication or exponential
Small constant jumps	Addition/Subtraction
1, 4, 9, 16...	Square numbers
1, 8, 27, 64...	Cube numbers
2, 3, 5, 7, 11...	Prime numbers
1, 1, 2, 3, 5, 8...	Fibonacci
1, 2, 6, 24, 120...	Factorials

Important Number Tables to Memorize

Squares (1-20)

n	n²	n	n²
1	1	11	121
2	4	12	144
3	9	13	169
4	16	14	196
5	25	15	225
6	36	16	256
7	49	17	289
8	64	18	324
9	81	19	361
10	100	20	400

Cubes (1-10)

n	n³
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000

📝 Practice Problems

Set 1: Letter Series

Q.No	Series	Options	Answer
1	B, D, F, H, ?	J, K, I, L	J
2	A, E, I, M, ?	P, Q, R, O	Q
3	Z, X, V, T, ?	R, S, Q, P	R
4	AC, EG, IK, ?	LM, MO, NP, OQ	MO
5	AZ, CX, EV, ?	GT, GU, HT, FT	GT

Set 2: Number Series

Q.No	Series	Options	Answer
1	2, 6, 18, 54, ?	108, 162, 148, 156	162
2	1, 4, 10, 22, ?	40, 44, 46, 48	46
3	3, 6, 11, 18, 27, ?	36, 38, 40, 42	38
4	2, 3, 5, 7, 11, ?	12, 13, 14, 15	13
5	1, 5, 14, 30, 55, ?	85, 91, 100, 110	91

Detailed Solutions

Solution 1 (Set 2, Q1):

Series: 2, 6, 18, 54, ?

Term	2	6	18	54	?
Ratio	—	×3	×3	×3	×3

Answer: 54 × 3 = 162 ✓

Solution 2 (Set 2, Q2):

Series: 1, 4, 10, 22, ?

Term	1	4	10	22	?
Difference	—	+3	+6	+12	+24
Pattern	—	×2	×2	×2	—

Answer: 22 + 24 = 46 ✓

Solution 3 (Set 2, Q3):

Series: 3, 6, 11, 18, 27, ?

Term	3	6	11	18	27	?
1st Diff	—	+3	+5	+7	+9	+11
2nd Diff	—	—	+2	+2	+2	+2

Answer: 27 + 11 = 38 ✓

📊 Summary Table

Concept	Key Points
Letter Series	Learn EJOTY, practice position calculations
Number Series	Master squares, cubes, primes, factorials
Alpha-Numeric	Combine letter and number patterns
Finding Patterns	Calculate differences, then difference of differences
Alternating Series	Check odd and even positions separately
Practice	Solve at least 50+ problems for mastery

✅ Final Checklist for Mastery

Memorize letter positions (EJOTY trick)
Know squares (1-20) and cubes (1-10)
Recognize prime numbers up to 50
Practice 10 problems daily
Time yourself (30-45 seconds per question)
Review mistakes and understand patterns

🎯 Pro Tips for Exams

Don't spend more than 1 minute on any series question
Start with the easiest pattern - check addition/subtraction first
If stuck, try options - substitute and verify
Practice mental math - speed matters
Look for familiar sequences - squares, cubes, factorials

Letter	Position	Letter	Position	Letter	Position
A	1	J	10	S	19
B	2	K	11	T	20
C	3	L	12	U	21
D	4	M	13	V	22
E	5	N	14	W	23
F	6	O	15	X	24
G	7	P	16	Y	25
H	8	Q	17	Z	26
I	9	R	18

n	n²	n	n²
1	1	11	121
2	4	12	144
3	9	13	169
4	16	14	196
5	25	15	225
6	36	16	256
7	49	17	289
8	64	18	324
9	81	19	361
10	100	20	400

Letter	Position	Letter	Position	Letter	Position
A	1	J	10	S	19
B	2	K	11	T	20
C	3	L	12	U	21
D	4	M	13	V	22
E	5	N	14	W	23
F	6	O	15	X	24
G	7	P	16	Y	25
H	8	Q	17	Z	26
I	9	R	18

n	n²	n	n²
1	1	11	121
2	4	12	144
3	9	13	169
4	16	14	196
5	25	15	225
6	36	16	256
7	49	17	289
8	64	18	324
9	81	19	361
10	100	20	400

Verbal Intelligence