In this kind of test, series of numbers or letters is given. One of the units in the series (either a number, a letter or a cluster of letters) is missing. The candidate is required to recognise the pattern of the series and to provide the missing digit or letter.
Number Series
Number series can be classified into the following types· Difference series:
a)Constant difference Ex: 1,4,7,10,13 ………
b)Increasing or Decreasing difference Ex: 2,3,5,8,12,17……..
· Product series:
Ex: 2,4,8,16,32…… Each number in the series is multiplied by 2 to get the next term
· Squares/Cubes series:
Ex: 1,4,9,16……… The numbers are squares of 1,2,3,4,…….
· Combination series:
Ex: 2,6,10,3,9,13,4,12,……….
2is multiplied by 3 to get next term & 4 is added to it to get third term. The next term
is 3 ( first term +1). It is multiplied by 3 to get 9 & then 4 is added to get 13.
Ex: 1,2,6,21,88………
The pattern is 1,1*1+1=2,2*2+2=6,6*3+3=21,21*4+4==88,……………….
· Miscellaneous:
Prime numbers: 3,5,7,11,13,17,……
Ex:9,25,49,121,169,…….. Squares of prime numbers
Ex:8,24,48,120,….. Squres of prime numbers – 1
In each of the following questions , there is a series with one term missng as shown by (?) . You have to find the missing number out of the five alternatives given below each question.
1) 1, 1, 2, 6, 24, ?, 720
(a) 100 (b104 (c) 108 (d) 120 (e) None
2) 212,179,146,113 ?
(a) 112 (b) 50 (c) 37 (d) 70 (e) 80
(a) 112 (b) 50 (c) 37 (d) 70 (e) 80
3) 17,36,53,68,?92
(a) 81 (b) 83 (c) 71 (d) 85 (e) None of these
In the following questions , each series contains a wrong term. You have to find out the wrong term.
4) 3,10,19,31,43,58, 75
5) 325,259,202,160,127,105,94
Letter Series
In these type of questions a few letters forming a series are given. The terms of the series may be formed by individual letters or clusters of letters. The sequence of letters follows a particular scheme. At one or at more places in the series one or some letters are missing. These missing letters are indicated by either a blank space or a mark of interrogation. You are required to study the scheme or pattern of the series of letters and supply the missing letter(S) out of the list of alternatives given below the series.
6) C B A E D Z G F ?
(a) X (b) H (c) Q (d) Y (e) None
7) AK EO IS ? QA UE
(a) HY (b) MW (c) AE (d) YZ (e) None
(a) 81 (b) 83 (c) 71 (d) 85 (e) None of these
In the following questions , each series contains a wrong term. You have to find out the wrong term.
4) 3,10,19,31,43,58, 75
5) 325,259,202,160,127,105,94
Letter Series
In these type of questions a few letters forming a series are given. The terms of the series may be formed by individual letters or clusters of letters. The sequence of letters follows a particular scheme. At one or at more places in the series one or some letters are missing. These missing letters are indicated by either a blank space or a mark of interrogation. You are required to study the scheme or pattern of the series of letters and supply the missing letter(S) out of the list of alternatives given below the series.
6) C B A E D Z G F ?
(a) X (b) H (c) Q (d) Y (e) None
7) AK EO IS ? QA UE
(a) HY (b) MW (c) AE (d) YZ (e) None
8) AC EG IK MO ?
(a) QS (b) DE (c) HJ (d) NP (e) None of these
(a) QS (b) DE (c) HJ (d) NP (e) None of these
9) aaa - bb - aab - baaa - bb
(a). babb (b). abab (c) bbaa (d) baab (e) None of these
(a). babb (b). abab (c) bbaa (d) baab (e) None of these
10) HS JQ LO NM ?
(a) GH (b) IJ (c) OP (d) KP (e) PK
ANSWERS
1) (d): The pattern is x 1, x 2, x 3, x 4,..... So, missing term = 24 x 5 = 120.
2) (e): In this series 33 is subtracted from each term to obtain the next term. so the next term is : 133 - 33 = 80
3) (a) : In this series the first number is added by 19 to obtain the second term and thereafter the number to be added to each term is decreased by 2. Thus 17 + 19= 36; 36 + 17=53; 53 +15=68; 68 + 13=81 and so on
4) (b): This series follows the pattern: 22 - 1, 32+1, 42 +3, 52 + 5, and so on. According to this pattern, the fourth term should be 30 not 31.
5) (b): In this series each term is obtained by subtracting respectively 66, 55, 44, 33, 22 and 11 from the previous term. Hense 202 is wrong. The corret answer is 204
6) (d): In this series, the third, sixth, and ninth letters are in reverse alphabetical order.
7) (c) : In each term of the given series, the first letter is moved three steps forward while the second letter is moved thre steps backward in order to obtain the next term.
8) (a): Here one letter has been skipped between the letters of each term and also between the second letter of a term and the first letter of the next term.
9) (a) : The series is aaa bbb aaa bbb aaa bbb
10) (e): In order to obtain the corresponding letters of the next term, the first latter of each term is moved two steps forward and the second letter is moved two steps backward.
An arithmetic progression is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
For example, the sequence 3, 5, 7, 9,11,.. is an arithmetic progression with common difference 2.
If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the n-th term of the sequence is given by
an = a1 + (n - 1)d, n = 1, 2, ...
The sum S of the first n values of a finite sequence is given by the formula:
S = 1/2(a1 + an)n, where a1 is the first term and an the last.
or
S = 1/2(2a1 + d(n-1))n
(a) GH (b) IJ (c) OP (d) KP (e) PK
ANSWERS
1) (d): The pattern is x 1, x 2, x 3, x 4,..... So, missing term = 24 x 5 = 120.
2) (e): In this series 33 is subtracted from each term to obtain the next term. so the next term is : 133 - 33 = 80
3) (a) : In this series the first number is added by 19 to obtain the second term and thereafter the number to be added to each term is decreased by 2. Thus 17 + 19= 36; 36 + 17=53; 53 +15=68; 68 + 13=81 and so on
4) (b): This series follows the pattern: 22 - 1, 32+1, 42 +3, 52 + 5, and so on. According to this pattern, the fourth term should be 30 not 31.
5) (b): In this series each term is obtained by subtracting respectively 66, 55, 44, 33, 22 and 11 from the previous term. Hense 202 is wrong. The corret answer is 204
6) (d): In this series, the third, sixth, and ninth letters are in reverse alphabetical order.
7) (c) : In each term of the given series, the first letter is moved three steps forward while the second letter is moved thre steps backward in order to obtain the next term.
8) (a): Here one letter has been skipped between the letters of each term and also between the second letter of a term and the first letter of the next term.
9) (a) : The series is aaa bbb aaa bbb aaa bbb
10) (e): In order to obtain the corresponding letters of the next term, the first latter of each term is moved two steps forward and the second letter is moved two steps backward.
PROGRESSIONS
Arithmetic ProgressionAn arithmetic progression is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
For example, the sequence 3, 5, 7, 9,11,.. is an arithmetic progression with common difference 2.
If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the n-th term of the sequence is given by
an = a1 + (n - 1)d, n = 1, 2, ...
The sum S of the first n values of a finite sequence is given by the formula:
S = 1/2(a1 + an)n, where a1 is the first term and an the last.
or
S = 1/2(2a1 + d(n-1))n
Geometric Progression
A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.a geometric sequence can be written as:
ar0=a, ar1=ar, ar2, r3, ... where r ≠ 0, q is the common ratio and a is a scale factor.
Formulae for the n-th term can be defined as:
an = an-1.r
an = a1.rn-1
The common ratio then is:
r = ak /ak-1
A sequence with a common ratio of 2 and a scale factor of 1 is 1, 2, 4, 8, 16, 32...
A sequence with a common ratio of -1 and a scale factor of 3 is 5, -5, 5, -5, 5, -5,...
Harmonic Progressions
A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progression.
e.g. 1/4, 1/9, 1/14, 1/19 are in H.P. since 4,9, 14, 19 are in A.P.
In general, the numbers 1/a, 1/(a+d), 1/(a+2d), ..., 1/(a+(n+1)d) are in H.P.
