Introduction

Series tests present numerical sequences that follow a logical rule which is based on elementary arithmetic. an initial sequence is given from which the rule is to be deduced. You are then asked to predict the next number that obeys the rule. The difficulty level of these questions can increase in two ways; first, the logic behind the sequence becomes less trivial and demands attention and creativity; second, the missing number can be positioned at an early stage, thus preventing you from deciphering the hidden rule by looking only at the previous numbers in the sequence. Moreover, a letter series test is also often asked which asks the applicant to identify the pattern between letter sets.



1. Examine the difference between adjacent numbers.

  • In a simple series, the difference between two consecutive numbers is number constant.

Example: 27, 24,21,18,...

Rule: There is a difference of  (-3) between each item. The missing number in this case is 15.

  • In a more complex series, the differences between numbers may be dynamic rather than fixed, but there still is a clear logical rule.
Example: 3, 4, 6, 9, 13, 18, ...

Rule: Add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2, and after the third number add 3, etc. In this case, the missing number is 24.

2. See whether there is a multiplication or division pattern between two adjacent numbers.

Example: 64, 32, 16, 8, ...

Rule: Divide each number by 2 to get the next number in the series. The missing number is 4.

3. Check whether adjacent numbers in the series change based on a logical pattern.

Example: 2, 4, 12, 48, ...

Rule: Multiply the first number by 2, the second number by 3 ad the third number by 4, etc. The missing item is 240.

4. See if you can find a rule that involves using two or more basic arithmetic functions (+-/*). In the below series, the functions alternate in an orderly fashion.

Example: 5, 7, 14, 16, 32, 34, ...

Rule: Add 2, multiply by 2, add by 2, multiply b 2, etc. The missing item is 68.

Tip: Series in this category are easy to identify. Just look at the numbers that do not appear to have a set pattern.

Important:

In a series that involves two more basic arithmetic functions, the differences between that you try to identify each pattern separately.

Example: 4, 6, 2, 8, 3, ...

Rule: In this series, the differences themselves create a series: +2, +3, *4,

The numbers advance by intervals of 1 and the arithmetic functions change in an orderly sequence. The next arithmetic function in the series should be +6, and so the next item in the series is 9 (3+6=9). 

Some solved questions with Explanation

1. 120, 99, 80, 63, 48, ?
(a) 35
(b) 38
(c) 39
(d) 40
Ans:- a. Because the Pattern is -21, -19, -17, -15, ... So, missing term  = 48-13= 35.

2. 589654237, 89654237, 8965432, 965423, ?
(a) 58965
(b) 65432
(c) 89654
(d) 96542
Ans:- d. Because the digits are removed one by one from the beginning and the end in order alternately so as to obtain the subsequent terms of the series.

3. 3, 10, 101,?
(a) 10101
(b) 10201
(c) 10202
(d) 11012
Ans:- c. Because each term in the series is obtained by one from the beginning and the end in order alternately so as to obtain the subsequent terms of the series.

4. 125, 80, 45, 20, ?
(a) 5
(b) 8
(c) 10
(d) 12
Ans:- a. Because the pattern is -45, -35, -25, ...
So, missing term = 20-15 = 5.

5. 1,1,4,8,9,27,16,?
(a) 32
(b) 64
(c) 81
(d) 256
Ans:- b. Because the series consists of squares and cubes of consecutive natural numbers i.e. 1^2, 1^3, 2^2, 2^3, 3^2, 3^3, 4^2, 4^3, 5^2, 5^3,... So, missing term  = 4^2 =64.

6. 1, 2, 3,6, 9, 18, ?, 54
(a) 18
(b) 27
(c) 36
(d)  81
Ans:- b. Because the pattern is x 2, x 3/2, x 2, x 3/2, x 2,....
So, missing term = 18* 3/2 = 27.

7. 2, 3, 3, 5, 10, 13, ?, 43, 172, 177
(a) 23
(b) 38
(c) 39
(d) 40
Ans:-c. Because the pattern is +1, *1, +2, *2, +3, *3, +4, *4, ....
So, missing term  = 13*3 = 39.