# Series

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## Introduction to Series

 Alphabetic series:There are 26 English alphabets as shown below. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 26 English alphabets are written in groups of 5 because it is easier to memorize the position of alphabets when written in this manner. Alphabets in bold have the following positions E - 5    J - 10    O - 15    T - 20    Y - 25 These 5 alphabets (E, J, O, T, and Y) can act as reference positions in order to memorize or to calculate the position of other alphabets. In order to answer questions regarding alphabetic series we have to identify a pattern used in the question. Examples of patterns (addition factor) used in series are given below: +3, +3, +3, +3,... Ex: A, E, I,... -2, -2, -2, -2,... Ex: D, A, X, U,... +1, -2, +1, -2,... Ex: A, C, Z, B,... +1, +2, +3, +1, +2, +3,... Ex: A, C, F, J, L, O, S... etc to name a few. Example 1: C, M, F, O, I, Q, L, ? Solution: The series specified above is made up of two series. First series is C, F, I, L second series is M, O, Q, ? So, 'S' comes in place of '?' Example 2: Find the next number in the following series 1, 4, 9, 16, 25, 36, ? Solution: The given series contains perfect squares of natural numbers. So, the next number in the series is the next perfect square i.e. 49. By thinking from a different point of view we can consider the difference between consecutive pairs of numbers. Difference between consecutive pairs of numbers is 3, 5, 7, 9, 11. Logically speaking the next difference should be 13. So, the next term in the series is 36 + 13 = 49. So, this means that we can follow any approach and we will arrive at the correct answer. Finding Position: Very common type of questions that you will be seeing in exams ask you to find the position of alphabets from either the left side or from the right side. We may even get questions in exams in which we have to find the position of an alphabet with respect to the position of another alphabet. SHORTCUT: nth alphabet from the right = (26 - n + 1)th alphabet from left and vice versa. nth alphabet to the left of mth alphabet from the right = (m + n)th alphabet from right. nth alphabet to the right of mth alphabet from the right = (m - n)th alphabet from right. nth alphabet to the right of mth alphabet from the left = (m + n)th alphabet from left. nth alphabet to the left of mth alphabet from the left = (m - n)th alphabet from left.