# Series

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# Series

### Description

Arrangement/Series of numbers or alphabetical letters or combination of both are given, which are generally called the terms of the series. These terms follow a specific pattern all through the arrangement. The student is required to study the given arrangement, recognize the pattern followed in the arrangement and either finish the given arrangement with the most reasonable option or locate the wrong term in the arrangement.

### Concept

Series questions are divided into four types. They are: 1. Number series. 2. Alphabet series. 3. Alpha-numeric series. 4. Continuous pattern series. 1. Number series: Number series is sub divided into two cases. They are: 1. Completing the given series by finding the missing terms. 2. Finding the wrong term in the given series. 2. Alphabet series: A series of single, pairs or gatherings of letters or mixes of letters and numerals is given. The terms of the arrangement form a specific pattern as regards the position of letters in the English letters in order. The student is required to convert this pattern and according locate the missing term or the wrong term in the given series. 3. Alpha-numeric series: A jumbled type of questions of type 1 and type 2. Here, the terms of the given series are a mix of letters and numerals, which move as indicated by a set pattern. 4. Continuous pattern series: Comprises of a series of a small letters which take after a specific pattern. In any case, some letters are absent from the series. These missing letters are then given in an appropriate sequence as one of the choices. The applicant is required to choose this option as the answer.

### Model Problems

Model 1: What is the missing term in the given sequence: 1, 3, 3, 6, 7, 9, ?, 12, 21 Solution:
Given sequence is : 1, 3, 3, 6, 7, 9, ?, 12, 21 Notice that the given sequence is a combination of two series i.e. Let I: 1, 3, 7, ?, 21 II: 3, 6, 9, 12 In I, the pattern followed is +2, +4, .. and the pattern followed in II is + 3. Now, the missing number is 7 + 6 = 13 Therefore, the sequence is 1, 3, 3, 6, 7, 9, 13, 12, 21.
Model 2: Identify the wrong number in the series: 75, 36, 19, 10, 6 Solution:
Given series is 75, 36, 19, 10, 6 By observing the series clearly, each term is one more than the product of the digits of the preceding term. I.e. (7 x 5) + 1 = 36 (3 x 6) + 1 = 19 (1 x 9) + 1 = 10 (1 x 0) + 1 = 1 Therefore, 6 is the wrong number and must be replaced by 1.
Model 3: What are the next two terms in the series B, D, G, K, ?, ? Solution:
Given series is B, D, G, K, ?, ? Here, the first , second, third,.... letters of the series are respectively moved two, three, four, ... steps forward to obtain the successive terms of the series. Thus, the fifth term in the series must be a letter which is five steps ahead of K i.e. P, The sixth term must be a letter six steps ahead of P i.e. V. So, the next terms are P and V. Therefore, series is B, D, G, K, P, V.
Model 4: Find the next term in the alpha numeric series: W1C, U2F, S6I, Q21L, O88O, M445R, ? Solution:
Given series is : W1C, U2F, S6I, Q21L, O88O, M445R, ? 1st letter: W → U → S → Q → O → M → K Here, the gap is -2 in between the letters. So, the letter in desired term is K. 2nd letter: C → F → I → L → O → R → U Here, the gap is +3 in between the letters.So, the letter in desired term is U. Now, The series formed by numerals is 1, 2, 6, 21, 88, 445, .... Numbers follows the pattern i.e. 1 x 1 + 1 = 2 2 x 2 + 2 = 6 6 x 3 + 3 = 21 21 x 4 + 4 = 88 88 x 5 + 5 = 445 So, the numeral in the desired term = 445 x 6 + 6 = 2676. Therefore, the desired and next term in the series is K2676U.
Model 5: In the following series, choose the alternative which contains the numerals to be filled in the vacant spaces marked by "?", in the correct order: C B _ _ D _ B A B C C B _ _ 1 2 4 3 _ _ ? ? ? ? a _ a b _ c _ b _ _ _ _ a) 3, 4, 4, 3 b) 3, 2, 2, 3 c) 3, 1, 1, 3 d) 1, 4, 4, 1 Solution:
Given series is: C B _ _ D _ B A B C C B _ _ 1 2 4 3 _ _ ? ? ? ? a _ a b _ c _ b _ _ _ _ By comparing the positions of the capital letters, numbers and small letters, a corresponds to c. 1 corresponds to a. Hence, a and 1 corresponds to C. b corresponds to A. 2 corresponds to b. Hence, b and 2 corresponds to A. Also, 4 corresponds to D. Remaining number i.e. 3 corresponds to B. Therefore, BCCB corresponds to 3, 1, 1, 3.