PPT: Series | Logical Reasoning for CLAT PDF Download

 Page 1


Series and 
Sequences
Page 2


Series and 
Sequences
What is a Series / Sequence?
Basic Definition
A series or sequence consists of 
several terms, with each term 
having its own importance. There 
exists a certain relationship 
between consecutive or 
alternating terms that repeats 
throughout the series.
Types of Series
Based on their composition, series 
can be classified into three main 
types: Number series, Alphabet 
series, and Mixed series. Each 
type follows specific patterns that 
can be identified with practice.
Mixed Series Complexity
Mixed series comprise letters, numbers, and symbols. Unlike alphabet 
series, the number of terms isn't fixed and may contain any number of 
terms. These require sufficient practice as there are no definite shortcuts.
Page 3


Series and 
Sequences
What is a Series / Sequence?
Basic Definition
A series or sequence consists of 
several terms, with each term 
having its own importance. There 
exists a certain relationship 
between consecutive or 
alternating terms that repeats 
throughout the series.
Types of Series
Based on their composition, series 
can be classified into three main 
types: Number series, Alphabet 
series, and Mixed series. Each 
type follows specific patterns that 
can be identified with practice.
Mixed Series Complexity
Mixed series comprise letters, numbers, and symbols. Unlike alphabet 
series, the number of terms isn't fixed and may contain any number of 
terms. These require sufficient practice as there are no definite shortcuts.
Numerical Series
Pure Series
In this type, numbers follow a 
pattern that can be easily 
understood. The numbers 
themselves may be perfect 
squares, perfect cubes, prime 
numbers, or combinations of 
these.
Difference Series
The difference between 
consecutive numbers forms a 
pattern. For example, in the 
series 1, 3, 5, 7, 9, 11, the 
difference between 
consecutive numbers is 
consistently 2.
Progressive Difference
Sometimes the differences 
themselves follow a pattern. In 
the series 1, 2, 4, 7, 11, 16, the 
differences between 
consecutive numbers are 1, 2, 
3, 4, 5, forming their own 
sequence.
Page 4


Series and 
Sequences
What is a Series / Sequence?
Basic Definition
A series or sequence consists of 
several terms, with each term 
having its own importance. There 
exists a certain relationship 
between consecutive or 
alternating terms that repeats 
throughout the series.
Types of Series
Based on their composition, series 
can be classified into three main 
types: Number series, Alphabet 
series, and Mixed series. Each 
type follows specific patterns that 
can be identified with practice.
Mixed Series Complexity
Mixed series comprise letters, numbers, and symbols. Unlike alphabet 
series, the number of terms isn't fixed and may contain any number of 
terms. These require sufficient practice as there are no definite shortcuts.
Numerical Series
Pure Series
In this type, numbers follow a 
pattern that can be easily 
understood. The numbers 
themselves may be perfect 
squares, perfect cubes, prime 
numbers, or combinations of 
these.
Difference Series
The difference between 
consecutive numbers forms a 
pattern. For example, in the 
series 1, 3, 5, 7, 9, 11, the 
difference between 
consecutive numbers is 
consistently 2.
Progressive Difference
Sometimes the differences 
themselves follow a pattern. In 
the series 1, 2, 4, 7, 11, 16, the 
differences between 
consecutive numbers are 1, 2, 
3, 4, 5, forming their own 
sequence.
Solved Examples of Numerical Series
1
Example 1: 1, 5, 13, 29, ___, 
125
The series increases by +4, +8, 
+16, +32, +64. Adding 32 to 29 
gives 61, which is the missing 
number. The pattern follows a 
geometric progression in the 
differences.
2
Example 2: 1, 4, 9, 16, 25, ___
These numbers are perfect 
squares: 1², 2², 3², 4², 5². Therefore, 
the next number is 6² = 36, 
continuing the pattern of square 
numbers.
3
Example 3: 6, 11, 21, 36, 56, 
___
The series progresses by adding 5, 
10, 15, 20, 25. Adding 25 to 56 
gives 81 as the next number, 
following the pattern of increasing 
differences.
Page 5


Series and 
Sequences
What is a Series / Sequence?
Basic Definition
A series or sequence consists of 
several terms, with each term 
having its own importance. There 
exists a certain relationship 
between consecutive or 
alternating terms that repeats 
throughout the series.
Types of Series
Based on their composition, series 
can be classified into three main 
types: Number series, Alphabet 
series, and Mixed series. Each 
type follows specific patterns that 
can be identified with practice.
Mixed Series Complexity
Mixed series comprise letters, numbers, and symbols. Unlike alphabet 
series, the number of terms isn't fixed and may contain any number of 
terms. These require sufficient practice as there are no definite shortcuts.
Numerical Series
Pure Series
In this type, numbers follow a 
pattern that can be easily 
understood. The numbers 
themselves may be perfect 
squares, perfect cubes, prime 
numbers, or combinations of 
these.
Difference Series
The difference between 
consecutive numbers forms a 
pattern. For example, in the 
series 1, 3, 5, 7, 9, 11, the 
difference between 
consecutive numbers is 
consistently 2.
Progressive Difference
Sometimes the differences 
themselves follow a pattern. In 
the series 1, 2, 4, 7, 11, 16, the 
differences between 
consecutive numbers are 1, 2, 
3, 4, 5, forming their own 
sequence.
Solved Examples of Numerical Series
1
Example 1: 1, 5, 13, 29, ___, 
125
The series increases by +4, +8, 
+16, +32, +64. Adding 32 to 29 
gives 61, which is the missing 
number. The pattern follows a 
geometric progression in the 
differences.
2
Example 2: 1, 4, 9, 16, 25, ___
These numbers are perfect 
squares: 1², 2², 3², 4², 5². Therefore, 
the next number is 6² = 36, 
continuing the pattern of square 
numbers.
3
Example 3: 6, 11, 21, 36, 56, 
___
The series progresses by adding 5, 
10, 15, 20, 25. Adding 25 to 56 
gives 81 as the next number, 
following the pattern of increasing 
differences.
Solved Examples of 
Alphabet Series
Example 5: A, B, 
C, D, E, (&), (&)
This series consists 
of alphabets in their 
original order. The 
missing terms 
would be F and G, 
simply continuing 
the alphabetical 
sequence.
Example 6: Z, X, 
V, T, R, (&), (&)
This series consists 
of alternate letters 
in reverse order, 
skipping one letter 
each time. The 
missing terms 
would be P and N, 
continuing the 
pattern backward.
Example 7: B, D, 
G, K, P, (&)
Each time the 
number of letters 
skipped increases 
by one. B is 2nd, D 
is 4th, G is 7th, K is 
11th, P is 16th, so 
the next will be 
22nd, which is V.