ICAI Notes- Number Series, Coding and Decoding and Odd Man Out | Quantitative Aptitude for CA Foundation PDF Download

 Page 1


w This Section deals with questions on which series or letters in some order, Coding and decoding 
w These terms of the series or letters are follows certain pattern throughout
9
CHAPTER
NUMBER SERIES, CODING DECODING 
AND ODD MAN OUT SERIES 
LEARNING OBJECTIVES
 9.1 SERIES
Series Classified into Two Types, Namely
A. Number Series
B. Alphabet Series
A. NUMBER SERIES
Case 1: Missing terms of the series
In these type the questions we have to identify the missing term of the series according to a specific 
pattern of the series rule to form its code. The students are required to detect the missing number of 
the series and answer the questions accordingly.
Example 1: Find the missing term of the series 2, 7, 16, ______ , 46, 67, 92
Explanation: Here the terms of the series are +5, +9, +13, +17, +21 , +25…
Thus, 2 + 5 = 7; and 7 + 9 = 16 …
So missing term = 16 + 13 = 29
Example 2: Find the wrong terms of the series 9, 29, 65, 126, 217, 344
Explanation: 2
3
+1; 3
3 
+ 1; 4
3 
+ 1; 5
3
 + 1; 6
3
 + 1; 7
3
 + 1
Here 29 is wrong term of series
Example 3: Find the missing term of the series 1,9, 25, 49, 81, 121, .............
Solution: The given terms of the series consists square of consecutive odd number 1 , 3 , 5 , 7 , ....
2222
So missing value = 13
2 
= 169
© The Institute of Chartered Accountants of India
Page 2


w This Section deals with questions on which series or letters in some order, Coding and decoding 
w These terms of the series or letters are follows certain pattern throughout
9
CHAPTER
NUMBER SERIES, CODING DECODING 
AND ODD MAN OUT SERIES 
LEARNING OBJECTIVES
 9.1 SERIES
Series Classified into Two Types, Namely
A. Number Series
B. Alphabet Series
A. NUMBER SERIES
Case 1: Missing terms of the series
In these type the questions we have to identify the missing term of the series according to a specific 
pattern of the series rule to form its code. The students are required to detect the missing number of 
the series and answer the questions accordingly.
Example 1: Find the missing term of the series 2, 7, 16, ______ , 46, 67, 92
Explanation: Here the terms of the series are +5, +9, +13, +17, +21 , +25…
Thus, 2 + 5 = 7; and 7 + 9 = 16 …
So missing term = 16 + 13 = 29
Example 2: Find the wrong terms of the series 9, 29, 65, 126, 217, 344
Explanation: 2
3
+1; 3
3 
+ 1; 4
3 
+ 1; 5
3
 + 1; 6
3
 + 1; 7
3
 + 1
Here 29 is wrong term of series
Example 3: Find the missing term of the series 1,9, 25, 49, 81, 121, .............
Solution: The given terms of the series consists square of consecutive odd number 1 , 3 , 5 , 7 , ....
2222
So missing value = 13
2 
= 169
© The Institute of Chartered Accountants of India
9.2
LOGICAL REASONING
B. ALPHABET SERIES
Alphabet series consists of letters of the alphabets placed in a specific pattern. For example, the series 
are in the following order of the numbers.
123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
A BC D E FG H I J K L M N O P Q R S T U V W X Y Z
26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 987654321
Example 4: Find the next term of the series BKS, DJT, FIU, HHV?
Explanation: In each term, the first letter is moved two steps forward, the second letter one step 
backward and third letter one step forward to obtain the corresponding letter of the next term. So the 
missing term is JGW.
C. LETTER SERIES: 
These type of question usually consist of a series of small letters which follow a certain pattern. 
However some letters are missing from the series. These missing letters are then given in a proper 
sequence as one of the alternatives.
Example 5: aab, ____, aaa, bba, ____
(a) baa (b) abb (c) bab (d) aab
1) The first blank space should be filled in by ‘b’ so that we have two a’s by two b’s.
2) The second blank place should be  `a’, so that we have three a’s followed by three b’s. 
3) The last space must be filled in by ‘a’.
4) Thus we have two possible answers – ‘baa’and ‘bba’.
5) But only ‘baa’appears in the alternatives.
So the answer (a) is correct.
 9.2 CODING AND DECODING
Before transmitting, the data is encoded and at receiver side encode data is decoded in order to obtain 
original data by determining common key in encoded data.
The Coding and Decoding is classified into the following types.
Type 1:  Letter Coding
Type 2:  Number Coding
Type 1: Letter Coding
In these type the real alphabets in a word are replaced by certain other alphabets according to a specific 
rule to form its code. The candidate is required to detect the common rule and answer the questions 
accordingly.
© The Institute of Chartered Accountants of India
Page 3


w This Section deals with questions on which series or letters in some order, Coding and decoding 
w These terms of the series or letters are follows certain pattern throughout
9
CHAPTER
NUMBER SERIES, CODING DECODING 
AND ODD MAN OUT SERIES 
LEARNING OBJECTIVES
 9.1 SERIES
Series Classified into Two Types, Namely
A. Number Series
B. Alphabet Series
A. NUMBER SERIES
Case 1: Missing terms of the series
In these type the questions we have to identify the missing term of the series according to a specific 
pattern of the series rule to form its code. The students are required to detect the missing number of 
the series and answer the questions accordingly.
Example 1: Find the missing term of the series 2, 7, 16, ______ , 46, 67, 92
Explanation: Here the terms of the series are +5, +9, +13, +17, +21 , +25…
Thus, 2 + 5 = 7; and 7 + 9 = 16 …
So missing term = 16 + 13 = 29
Example 2: Find the wrong terms of the series 9, 29, 65, 126, 217, 344
Explanation: 2
3
+1; 3
3 
+ 1; 4
3 
+ 1; 5
3
 + 1; 6
3
 + 1; 7
3
 + 1
Here 29 is wrong term of series
Example 3: Find the missing term of the series 1,9, 25, 49, 81, 121, .............
Solution: The given terms of the series consists square of consecutive odd number 1 , 3 , 5 , 7 , ....
2222
So missing value = 13
2 
= 169
© The Institute of Chartered Accountants of India
9.2
LOGICAL REASONING
B. ALPHABET SERIES
Alphabet series consists of letters of the alphabets placed in a specific pattern. For example, the series 
are in the following order of the numbers.
123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
A BC D E FG H I J K L M N O P Q R S T U V W X Y Z
26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 987654321
Example 4: Find the next term of the series BKS, DJT, FIU, HHV?
Explanation: In each term, the first letter is moved two steps forward, the second letter one step 
backward and third letter one step forward to obtain the corresponding letter of the next term. So the 
missing term is JGW.
C. LETTER SERIES: 
These type of question usually consist of a series of small letters which follow a certain pattern. 
However some letters are missing from the series. These missing letters are then given in a proper 
sequence as one of the alternatives.
Example 5: aab, ____, aaa, bba, ____
(a) baa (b) abb (c) bab (d) aab
1) The first blank space should be filled in by ‘b’ so that we have two a’s by two b’s.
2) The second blank place should be  `a’, so that we have three a’s followed by three b’s. 
3) The last space must be filled in by ‘a’.
4) Thus we have two possible answers – ‘baa’and ‘bba’.
5) But only ‘baa’appears in the alternatives.
So the answer (a) is correct.
 9.2 CODING AND DECODING
Before transmitting, the data is encoded and at receiver side encode data is decoded in order to obtain 
original data by determining common key in encoded data.
The Coding and Decoding is classified into the following types.
Type 1:  Letter Coding
Type 2:  Number Coding
Type 1: Letter Coding
In these type the real alphabets in a word are replaced by certain other alphabets according to a specific 
rule to form its code. The candidate is required to detect the common rule and answer the questions 
accordingly.
© The Institute of Chartered Accountants of India
9.3
NUMBER SERIES, CODING DECODING AND ODD MAN OUT SERIES
Case1: To form the code for another word
Example 6: If in a certain language MYSTIFY is coded as NZTUJGZ, how is MENESIS coded in that 
language?
Explanation: Clearly, each letter in the word MYSTIFY is moved one step forward to obtain the 
corresponding letter of the code.
M Y S T I F Y
+1 
?
N Z T U J G Z
So, in MENESIS, N will be coded as O, E as F, M as N and so on. Thus, the code becomes NFOFTJT.
Example 7: If TAP is coded as SZO, then how is FRIEND coded? 
Explanation: Clearly each letter in the word TAP is moved one step backward to obtain the 
corresponding letter of the code.
S Z O
-1 
?
T A P
Thus, in FRIEND, F will be coded as E, R as Q , I as H, E as D, N as M and D as C. So, the code becomes 
EQHDMC.
Example 8: In a certain code, MENTION is written as LNEITNO. How is PRESENT written in that 
code? 
Explanation: Clearly, to obtain the code, the first letter of the word MENTION is moved one step 
backward and the remaining letters are Reversed in order, taking two at a time. So, in PRESENT,
 P will be coded as O, and the sequence of the remaining letter in the code would be ERESTN. Thus
 the code becomes OERESTN. Hence, The answer is OERESTN.
Case 2: To find the word by analysing the given code (DECODING)
Example 9: If in a certain language CARROM is coded as BZQQNL, which word will be coded as 
HORSE?
Explanation: Each letter of the word is one step ahead of the corresponding letter of the code
    B Z Q Q N L  H O R S E
    | | |  |  | |   | |  | | |
    C A R R O M   I  P   S T F
 So, H is coded as I, O as P , R as S, S as T and E as F. HORSE is coded a IPSTF.
Type 2: Number Coding
In these questions, either numerical code values are assigned to a word or alphabetical code letters 
are assigned to the numbers. The candidate is required to analyse the code as per the directions.
© The Institute of Chartered Accountants of India
Page 4


w This Section deals with questions on which series or letters in some order, Coding and decoding 
w These terms of the series or letters are follows certain pattern throughout
9
CHAPTER
NUMBER SERIES, CODING DECODING 
AND ODD MAN OUT SERIES 
LEARNING OBJECTIVES
 9.1 SERIES
Series Classified into Two Types, Namely
A. Number Series
B. Alphabet Series
A. NUMBER SERIES
Case 1: Missing terms of the series
In these type the questions we have to identify the missing term of the series according to a specific 
pattern of the series rule to form its code. The students are required to detect the missing number of 
the series and answer the questions accordingly.
Example 1: Find the missing term of the series 2, 7, 16, ______ , 46, 67, 92
Explanation: Here the terms of the series are +5, +9, +13, +17, +21 , +25…
Thus, 2 + 5 = 7; and 7 + 9 = 16 …
So missing term = 16 + 13 = 29
Example 2: Find the wrong terms of the series 9, 29, 65, 126, 217, 344
Explanation: 2
3
+1; 3
3 
+ 1; 4
3 
+ 1; 5
3
 + 1; 6
3
 + 1; 7
3
 + 1
Here 29 is wrong term of series
Example 3: Find the missing term of the series 1,9, 25, 49, 81, 121, .............
Solution: The given terms of the series consists square of consecutive odd number 1 , 3 , 5 , 7 , ....
2222
So missing value = 13
2 
= 169
© The Institute of Chartered Accountants of India
9.2
LOGICAL REASONING
B. ALPHABET SERIES
Alphabet series consists of letters of the alphabets placed in a specific pattern. For example, the series 
are in the following order of the numbers.
123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
A BC D E FG H I J K L M N O P Q R S T U V W X Y Z
26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 987654321
Example 4: Find the next term of the series BKS, DJT, FIU, HHV?
Explanation: In each term, the first letter is moved two steps forward, the second letter one step 
backward and third letter one step forward to obtain the corresponding letter of the next term. So the 
missing term is JGW.
C. LETTER SERIES: 
These type of question usually consist of a series of small letters which follow a certain pattern. 
However some letters are missing from the series. These missing letters are then given in a proper 
sequence as one of the alternatives.
Example 5: aab, ____, aaa, bba, ____
(a) baa (b) abb (c) bab (d) aab
1) The first blank space should be filled in by ‘b’ so that we have two a’s by two b’s.
2) The second blank place should be  `a’, so that we have three a’s followed by three b’s. 
3) The last space must be filled in by ‘a’.
4) Thus we have two possible answers – ‘baa’and ‘bba’.
5) But only ‘baa’appears in the alternatives.
So the answer (a) is correct.
 9.2 CODING AND DECODING
Before transmitting, the data is encoded and at receiver side encode data is decoded in order to obtain 
original data by determining common key in encoded data.
The Coding and Decoding is classified into the following types.
Type 1:  Letter Coding
Type 2:  Number Coding
Type 1: Letter Coding
In these type the real alphabets in a word are replaced by certain other alphabets according to a specific 
rule to form its code. The candidate is required to detect the common rule and answer the questions 
accordingly.
© The Institute of Chartered Accountants of India
9.3
NUMBER SERIES, CODING DECODING AND ODD MAN OUT SERIES
Case1: To form the code for another word
Example 6: If in a certain language MYSTIFY is coded as NZTUJGZ, how is MENESIS coded in that 
language?
Explanation: Clearly, each letter in the word MYSTIFY is moved one step forward to obtain the 
corresponding letter of the code.
M Y S T I F Y
+1 
?
N Z T U J G Z
So, in MENESIS, N will be coded as O, E as F, M as N and so on. Thus, the code becomes NFOFTJT.
Example 7: If TAP is coded as SZO, then how is FRIEND coded? 
Explanation: Clearly each letter in the word TAP is moved one step backward to obtain the 
corresponding letter of the code.
S Z O
-1 
?
T A P
Thus, in FRIEND, F will be coded as E, R as Q , I as H, E as D, N as M and D as C. So, the code becomes 
EQHDMC.
Example 8: In a certain code, MENTION is written as LNEITNO. How is PRESENT written in that 
code? 
Explanation: Clearly, to obtain the code, the first letter of the word MENTION is moved one step 
backward and the remaining letters are Reversed in order, taking two at a time. So, in PRESENT,
 P will be coded as O, and the sequence of the remaining letter in the code would be ERESTN. Thus
 the code becomes OERESTN. Hence, The answer is OERESTN.
Case 2: To find the word by analysing the given code (DECODING)
Example 9: If in a certain language CARROM is coded as BZQQNL, which word will be coded as 
HORSE?
Explanation: Each letter of the word is one step ahead of the corresponding letter of the code
    B Z Q Q N L  H O R S E
    | | |  |  | |   | |  | | |
    C A R R O M   I  P   S T F
 So, H is coded as I, O as P , R as S, S as T and E as F. HORSE is coded a IPSTF.
Type 2: Number Coding
In these questions, either numerical code values are assigned to a word or alphabetical code letters 
are assigned to the numbers. The candidate is required to analyse the code as per the directions.
© The Institute of Chartered Accountants of India
9.4
LOGICAL REASONING
Case 1: When a numerical code values are assigned to words.
Example 10: If in a certain language A is coded as 1, B is coded as 2, and so on, how is AICCI is coded 
in that code? 
Explanation: As given the letters are coded as
 A B C D E F G H I
 1 2 3 4 5 6 7 8 9
So in AICCI, A is coded as 1, I as 9,and C as 3. Thus, AICCI is coded as 19339.
Example 11: If PAINT is coded as 74128 and EXCEL is coded as 93596, then how would you encode 
ANCIENT ? 
Explanation: Clearly, in the given code, the alphabets are coded as follows:
 P A I N T E X C L
  7 4 1 2 8 9 3 5 6
So, in ANCIENT, A is coded as 4, N is coded as 2, C as 5, I is coded as 1, E as 9, and T as 8. Hence, the 
correct code is 4251928.
Case 2: Number to letter coding.
Example 12: In a certain code, 2 is coded as P , 3 as N, 9 as Q, 5 as R, 4 as A and 6 as B. How is 423599 
coded in that code?
Explanation: Clearly as given, 4 as A, 2 as P , 3 as N and 5 is coded as R, 9 as Q. So, 423599 is coded as 
APNRQQ.
 9.3 ODD MAN OUT
Classification means ‘to assort the items’ of a given group on the basis of a certain common quality 
they possess and then spot the stranger or ‘odd one out’.
These questions are based on words, letters and numerals. In these types of problems, we consider 
the defining quality of particular things. In these questions, four or five elements are given, out of 
which one does not belong to the group. You are required to find the ’odd one’.
Example 13:  January, May, July, November 
(a) January    (b) May   (c) July  (d) November 
Explanation: All the months above are 31 days , whereas , November 30 days 
Answer: (d)
Example 14: 10, 14, 16, 18, 23, 24 and 26 
(a) 26     (b) 17    (c) 23   (d) 9 
Explanation: Each of the above series are even number, except 23. 
Answer: (c)
Example 15: 6, 9, 15, 21, 24, 26, 30 
(a) 9     (b) 26    (c) 24   (d) 30
© The Institute of Chartered Accountants of India
Page 5


w This Section deals with questions on which series or letters in some order, Coding and decoding 
w These terms of the series or letters are follows certain pattern throughout
9
CHAPTER
NUMBER SERIES, CODING DECODING 
AND ODD MAN OUT SERIES 
LEARNING OBJECTIVES
 9.1 SERIES
Series Classified into Two Types, Namely
A. Number Series
B. Alphabet Series
A. NUMBER SERIES
Case 1: Missing terms of the series
In these type the questions we have to identify the missing term of the series according to a specific 
pattern of the series rule to form its code. The students are required to detect the missing number of 
the series and answer the questions accordingly.
Example 1: Find the missing term of the series 2, 7, 16, ______ , 46, 67, 92
Explanation: Here the terms of the series are +5, +9, +13, +17, +21 , +25…
Thus, 2 + 5 = 7; and 7 + 9 = 16 …
So missing term = 16 + 13 = 29
Example 2: Find the wrong terms of the series 9, 29, 65, 126, 217, 344
Explanation: 2
3
+1; 3
3 
+ 1; 4
3 
+ 1; 5
3
 + 1; 6
3
 + 1; 7
3
 + 1
Here 29 is wrong term of series
Example 3: Find the missing term of the series 1,9, 25, 49, 81, 121, .............
Solution: The given terms of the series consists square of consecutive odd number 1 , 3 , 5 , 7 , ....
2222
So missing value = 13
2 
= 169
© The Institute of Chartered Accountants of India
9.2
LOGICAL REASONING
B. ALPHABET SERIES
Alphabet series consists of letters of the alphabets placed in a specific pattern. For example, the series 
are in the following order of the numbers.
123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
A BC D E FG H I J K L M N O P Q R S T U V W X Y Z
26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 987654321
Example 4: Find the next term of the series BKS, DJT, FIU, HHV?
Explanation: In each term, the first letter is moved two steps forward, the second letter one step 
backward and third letter one step forward to obtain the corresponding letter of the next term. So the 
missing term is JGW.
C. LETTER SERIES: 
These type of question usually consist of a series of small letters which follow a certain pattern. 
However some letters are missing from the series. These missing letters are then given in a proper 
sequence as one of the alternatives.
Example 5: aab, ____, aaa, bba, ____
(a) baa (b) abb (c) bab (d) aab
1) The first blank space should be filled in by ‘b’ so that we have two a’s by two b’s.
2) The second blank place should be  `a’, so that we have three a’s followed by three b’s. 
3) The last space must be filled in by ‘a’.
4) Thus we have two possible answers – ‘baa’and ‘bba’.
5) But only ‘baa’appears in the alternatives.
So the answer (a) is correct.
 9.2 CODING AND DECODING
Before transmitting, the data is encoded and at receiver side encode data is decoded in order to obtain 
original data by determining common key in encoded data.
The Coding and Decoding is classified into the following types.
Type 1:  Letter Coding
Type 2:  Number Coding
Type 1: Letter Coding
In these type the real alphabets in a word are replaced by certain other alphabets according to a specific 
rule to form its code. The candidate is required to detect the common rule and answer the questions 
accordingly.
© The Institute of Chartered Accountants of India
9.3
NUMBER SERIES, CODING DECODING AND ODD MAN OUT SERIES
Case1: To form the code for another word
Example 6: If in a certain language MYSTIFY is coded as NZTUJGZ, how is MENESIS coded in that 
language?
Explanation: Clearly, each letter in the word MYSTIFY is moved one step forward to obtain the 
corresponding letter of the code.
M Y S T I F Y
+1 
?
N Z T U J G Z
So, in MENESIS, N will be coded as O, E as F, M as N and so on. Thus, the code becomes NFOFTJT.
Example 7: If TAP is coded as SZO, then how is FRIEND coded? 
Explanation: Clearly each letter in the word TAP is moved one step backward to obtain the 
corresponding letter of the code.
S Z O
-1 
?
T A P
Thus, in FRIEND, F will be coded as E, R as Q , I as H, E as D, N as M and D as C. So, the code becomes 
EQHDMC.
Example 8: In a certain code, MENTION is written as LNEITNO. How is PRESENT written in that 
code? 
Explanation: Clearly, to obtain the code, the first letter of the word MENTION is moved one step 
backward and the remaining letters are Reversed in order, taking two at a time. So, in PRESENT,
 P will be coded as O, and the sequence of the remaining letter in the code would be ERESTN. Thus
 the code becomes OERESTN. Hence, The answer is OERESTN.
Case 2: To find the word by analysing the given code (DECODING)
Example 9: If in a certain language CARROM is coded as BZQQNL, which word will be coded as 
HORSE?
Explanation: Each letter of the word is one step ahead of the corresponding letter of the code
    B Z Q Q N L  H O R S E
    | | |  |  | |   | |  | | |
    C A R R O M   I  P   S T F
 So, H is coded as I, O as P , R as S, S as T and E as F. HORSE is coded a IPSTF.
Type 2: Number Coding
In these questions, either numerical code values are assigned to a word or alphabetical code letters 
are assigned to the numbers. The candidate is required to analyse the code as per the directions.
© The Institute of Chartered Accountants of India
9.4
LOGICAL REASONING
Case 1: When a numerical code values are assigned to words.
Example 10: If in a certain language A is coded as 1, B is coded as 2, and so on, how is AICCI is coded 
in that code? 
Explanation: As given the letters are coded as
 A B C D E F G H I
 1 2 3 4 5 6 7 8 9
So in AICCI, A is coded as 1, I as 9,and C as 3. Thus, AICCI is coded as 19339.
Example 11: If PAINT is coded as 74128 and EXCEL is coded as 93596, then how would you encode 
ANCIENT ? 
Explanation: Clearly, in the given code, the alphabets are coded as follows:
 P A I N T E X C L
  7 4 1 2 8 9 3 5 6
So, in ANCIENT, A is coded as 4, N is coded as 2, C as 5, I is coded as 1, E as 9, and T as 8. Hence, the 
correct code is 4251928.
Case 2: Number to letter coding.
Example 12: In a certain code, 2 is coded as P , 3 as N, 9 as Q, 5 as R, 4 as A and 6 as B. How is 423599 
coded in that code?
Explanation: Clearly as given, 4 as A, 2 as P , 3 as N and 5 is coded as R, 9 as Q. So, 423599 is coded as 
APNRQQ.
 9.3 ODD MAN OUT
Classification means ‘to assort the items’ of a given group on the basis of a certain common quality 
they possess and then spot the stranger or ‘odd one out’.
These questions are based on words, letters and numerals. In these types of problems, we consider 
the defining quality of particular things. In these questions, four or five elements are given, out of 
which one does not belong to the group. You are required to find the ’odd one’.
Example 13:  January, May, July, November 
(a) January    (b) May   (c) July  (d) November 
Explanation: All the months above are 31 days , whereas , November 30 days 
Answer: (d)
Example 14: 10, 14, 16, 18, 23, 24 and 26 
(a) 26     (b) 17    (c) 23   (d) 9 
Explanation: Each of the above series are even number, except 23. 
Answer: (c)
Example 15: 6, 9, 15, 21, 24, 26, 30 
(a) 9     (b) 26    (c) 24   (d) 30
© The Institute of Chartered Accountants of India
9.5
NUMBER SERIES, CODING DECODING AND ODD MAN OUT SERIES
Explanation: All are multiples of 3, except 26, answer (b) 
Answer: (b)
Example 16: 1, 5, 14, 30, 51, 55, 91
(a) 5    (b) 55    (c) 51   (d) 91 
Explanation: Each pattern is 1
2
, 1
2 
+ 2
2
, 1
2 
+ 2
2 
+ 3
2
, 1
2 
+ 2
2 
+ 3
2 
+ 4
2
, 1
2 
+ 2
2 
+ 3
2 
+ 4
2
+ 5
2
, 1
2 
+ 2
2 
+ 3
2 
+ 4
2 
+ 
5
2 
+ 6
2
 
But 51, is not of the form.
Answer: (c) 
Example 17: 16, 25, 36, 62, 144, 196, 225
(a) 36 (b) 62 (c) 196 (d) 144
Explanation:
Each of the number except 62, is a perfect square. 
Answer: (b) 
EXERCISE 9(A)
(Note: Questions are taken from previous exam questions papers of Competitive exams like SSC, 
RRB, MAT, UPSC etc.)
Choose the most appropriate answ    (a) or (b) or (c) or (d). 
1) 6, 11, 21, 36, 56 ?
 (a) 42   (b) 51  (c) 81 (d) 91
2) 10 , 100, 200, 310 ?
 (a) 400  
er
 (b) 410  (c) 420  (d) 430
3) 11, 13, 17, 19, 23, 25, 29 ?
 (a) 33   (b) 27  (c) 31  (d) 49
4) 6, 12, 21, 33 ?
 (a) 33   (b) 38  (c) 40  (d) 48 
5) 2, 5, 9, 14, ? , 27 
 (a) 20   (b) 16  (c) 18  (d) 24
6) 6, 11, 21, ? , 56, 81
 (a) 42   (b) 36  (c) 91  (d) 51
7) 10, 18, 28, 40, 54, ?, 88
 (a) 70   (b) 86  (c) 87 (d) 98
8) 120, 99, ?, 63, 48, 35
 (a) 80   (b)  36  (c)  45  (d) 40
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