Flashcards: Sequences and Series | Mathematics (Maths) for JEE Main & Advanced PDF Download

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SQUENCE, PROGRESSION AND SERIES 
A succession of numbers ?? 1
, ?? 2
, … ?? ?? formed according to the some definite rule is called sequence. "A 
sequence is a function of natural numbers with codomain as the set of Real numbers or complex 
numbers" 
Domain of sequence = ?? 
if Range of sequence ? ?? ? Real sequence 
if Range of sequence ? ?? ? Complex sequence 
 
Sequence is called finite or infinite depending upon its having number of terms as finite or infinite 
respectively. For example : 2,3,5,7,11, … is a sequence of prime numbers. It is an infinite sequence. 
  
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SQUENCE, PROGRESSION AND SERIES 
A succession of numbers ?? 1
, ?? 2
, … ?? ?? formed according to the some definite rule is called sequence. "A 
sequence is a function of natural numbers with codomain as the set of Real numbers or complex 
numbers" 
Domain of sequence = ?? 
if Range of sequence ? ?? ? Real sequence 
if Range of sequence ? ?? ? Complex sequence 
 
Sequence is called finite or infinite depending upon its having number of terms as finite or infinite 
respectively. For example : 2,3,5,7,11, … is a sequence of prime numbers. It is an infinite sequence. 
  
 
 
 
 
 
SQUENCE, PROGRESSION AND SERIES 
A progression is a sequence having its terms in a definite pattern e.g.: 1,4,9,16, ... is a progression as each 
successive term is obtained by squaring the next natural number. 
However a sequence may not always have an explicit formula of ?? th 
 term. 
Series is constructed by adding or subtracting the terms of a sequence e.g., 2 + 4 + 6 + 8 + ? . . + is a 
series. 
The term at ?? th 
 place is denoted by ?? ?? and is called general term of a sequence or progression or series. 
  
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SQUENCE, PROGRESSION AND SERIES 
A succession of numbers ?? 1
, ?? 2
, … ?? ?? formed according to the some definite rule is called sequence. "A 
sequence is a function of natural numbers with codomain as the set of Real numbers or complex 
numbers" 
Domain of sequence = ?? 
if Range of sequence ? ?? ? Real sequence 
if Range of sequence ? ?? ? Complex sequence 
 
Sequence is called finite or infinite depending upon its having number of terms as finite or infinite 
respectively. For example : 2,3,5,7,11, … is a sequence of prime numbers. It is an infinite sequence. 
  
 
 
 
 
 
SQUENCE, PROGRESSION AND SERIES 
A progression is a sequence having its terms in a definite pattern e.g.: 1,4,9,16, ... is a progression as each 
successive term is obtained by squaring the next natural number. 
However a sequence may not always have an explicit formula of ?? th 
 term. 
Series is constructed by adding or subtracting the terms of a sequence e.g., 2 + 4 + 6 + 8 + ? . . + is a 
series. 
The term at ?? th 
 place is denoted by ?? ?? and is called general term of a sequence or progression or series. 
  
 
 
 
 
 
 
ARITHMETIC PROGRESSION (A.P.) 
It is sequence in which the difference between any term and its just preceding term remains constant 
throughout. This constant is called the "common difference" of the A.P. and is denoted by ' ?? ' generally. 
A.P. is of the form ?? , (?? + ?? ), (?? + 2?? )… 
where ' ?? ' denotes the first term or initaial term 
  
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SQUENCE, PROGRESSION AND SERIES 
A succession of numbers ?? 1
, ?? 2
, … ?? ?? formed according to the some definite rule is called sequence. "A 
sequence is a function of natural numbers with codomain as the set of Real numbers or complex 
numbers" 
Domain of sequence = ?? 
if Range of sequence ? ?? ? Real sequence 
if Range of sequence ? ?? ? Complex sequence 
 
Sequence is called finite or infinite depending upon its having number of terms as finite or infinite 
respectively. For example : 2,3,5,7,11, … is a sequence of prime numbers. It is an infinite sequence. 
  
 
 
 
 
 
SQUENCE, PROGRESSION AND SERIES 
A progression is a sequence having its terms in a definite pattern e.g.: 1,4,9,16, ... is a progression as each 
successive term is obtained by squaring the next natural number. 
However a sequence may not always have an explicit formula of ?? th 
 term. 
Series is constructed by adding or subtracting the terms of a sequence e.g., 2 + 4 + 6 + 8 + ? . . + is a 
series. 
The term at ?? th 
 place is denoted by ?? ?? and is called general term of a sequence or progression or series. 
  
 
 
 
 
 
 
ARITHMETIC PROGRESSION (A.P.) 
It is sequence in which the difference between any term and its just preceding term remains constant 
throughout. This constant is called the "common difference" of the A.P. and is denoted by ' ?? ' generally. 
A.P. is of the form ?? , (?? + ?? ), (?? + 2?? )… 
where ' ?? ' denotes the first term or initaial term 
  
 
 
 
 
 
Important Relations : 
?? ?? - ?? ?? -1
= ?? = common difference 
?? ?? = ?? th 
 term of A.P. = {?? + (?? - 1)?? } = ?? ?? ?? '
= ?? th 
 term of A.P. from the end 
 = (?? - ?? + 1)
?? h
 term from beginning 
?? = total number of terms 
 i.e. , = ?? ?? '
= ?? (?? -?? +1)
= ?? + (?? - ?? )?? 
  
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SQUENCE, PROGRESSION AND SERIES 
A succession of numbers ?? 1
, ?? 2
, … ?? ?? formed according to the some definite rule is called sequence. "A 
sequence is a function of natural numbers with codomain as the set of Real numbers or complex 
numbers" 
Domain of sequence = ?? 
if Range of sequence ? ?? ? Real sequence 
if Range of sequence ? ?? ? Complex sequence 
 
Sequence is called finite or infinite depending upon its having number of terms as finite or infinite 
respectively. For example : 2,3,5,7,11, … is a sequence of prime numbers. It is an infinite sequence. 
  
 
 
 
 
 
SQUENCE, PROGRESSION AND SERIES 
A progression is a sequence having its terms in a definite pattern e.g.: 1,4,9,16, ... is a progression as each 
successive term is obtained by squaring the next natural number. 
However a sequence may not always have an explicit formula of ?? th 
 term. 
Series is constructed by adding or subtracting the terms of a sequence e.g., 2 + 4 + 6 + 8 + ? . . + is a 
series. 
The term at ?? th 
 place is denoted by ?? ?? and is called general term of a sequence or progression or series. 
  
 
 
 
 
 
 
ARITHMETIC PROGRESSION (A.P.) 
It is sequence in which the difference between any term and its just preceding term remains constant 
throughout. This constant is called the "common difference" of the A.P. and is denoted by ' ?? ' generally. 
A.P. is of the form ?? , (?? + ?? ), (?? + 2?? )… 
where ' ?? ' denotes the first term or initaial term 
  
 
 
 
 
 
Important Relations : 
?? ?? - ?? ?? -1
= ?? = common difference 
?? ?? = ?? th 
 term of A.P. = {?? + (?? - 1)?? } = ?? ?? ?? '
= ?? th 
 term of A.P. from the end 
 = (?? - ?? + 1)
?? h
 term from beginning 
?? = total number of terms 
 i.e. , = ?? ?? '
= ?? (?? -?? +1)
= ?? + (?? - ?? )?? 
  
 
 
 
 
 
Important Relations : 
?? ?? '
 = ?? ?? h
 term of A.P. from the end 
 = {?? - (?? - 1)?? }
?? ?? = the sum of first ?? terms of A.P. 
 =
?? 2
[2?? + (?? - 1)?? ] =
?? 2
[?? + ?? ]
 =
?? 2
[2?? - (?? - 1)?? ]
?? ?? = ?? ?? - ?? ?? -1