• #### Series

A series or sequence consists of several terms. In other words, the unit of a sequence are called TERMS. Each term in the series has its own importance as there exists certain relationship between the two consecutive / alternating terms. This relationship is repeated in the series and based on this relationship; we are required to find out the missing term. We come across several types of questions based on any given series. (Base on whether the series consist of the alphabets or the numerals (numbers) or the words, the series can be classified into the following types).

It is quite easy to decipher an alphabetic series as it is easy to remember the place of alphabet in the series. In case of number series also the pattern can be found out but in case of mixed series or jumbled series, it is very difficult to remember the position of each term.

A mixed series comprises letters, numbers and symbols and unlike the English alphabet series the number of terms is not fixed in such series. A mixed series may contain any number of terms viz. 23, 24, 26, 28, 30, 31 or 32. Such questions require sufficient practice as there are no definite SHORT CUTS for these questions. The questions on mixed series can be divided into two major heads:

1. Series of letters and numbers
2. Series of letters, numbers and symbols.

In questions based on mixed series one is required to judge and find out the relationship between the given terms and find out the answer. To begin with, count the terms and find out the relationship between the required terms.

### 1) NUMBER SERIES

#### Ex. 1. Which is the number that comes next in the sequence

1, 5, 13, 29, __ , 125

1) 32       2) 62       3) 61       4) 31       5) None of these

Sol. In this case the series is increasing by +4, +8, +16, +32, +64. So our answer is 61, as by adding the number 32 to 29 we get the required number i.e. 61.

#### Ex. 2. Which is the number that comes next in the sequence?

3, 7, 15, 31, 63, ?

1) 92       2) 115       3) 127       4) 131       5) None of these

Sol. Each number in the series is the preceding number multiplied by 2 and then increased by 1. Thus, (3 x 2) + 1 = 7, (7 x 2) + 1 = 15, (15 x 2) + 1 = 31 and so on

Missing number = (63 x 2) + 1 = 127 Hence the answer is (3)

### 2) ALPHABET SERIES

In problems based on alphabet series, the pattern of alphabet in the series is to be deducted and the next term is to be found out. There are no set rules, yet the problems can easily be solved if the place number of each alphabet is memorized. Like for K’s place value in the alphabet sequence is 11 and that of V is 22 , that of Q is 17 and X is 24. If these places are known, the questions become easy to solve.

There can be omission of alphabets one each time. Alphabets may be omitted in an increasing order or decreasing order; for example one each time or two each time or three each time and so on. There can also be alternate order such as first one alphabet is skipped, then two may be skipped and then three may be omitted. The skipping pattern may be

1. Regular Order: In this case the number of alphabets skipped remain the same through the series.
2. Increasing Order: Each time the number of alphabets skipped increase in a given pattern.

The theory can only be understood with the help of practical examples only.

#### Ex. 1. What terms will fill the blank spaces?

A, B, C , D, E, (……), (……)

1) O, K       2) N, M       3) K, S       4) M, N       5) F, G

Sol. : The given series consist of alphabets in their original order. So, the missing terms would be F and G. Ans. (5)

#### Ex. 2. What terms will fill the blank spaces?

Z, X, V, T, R, (……), (……)

1) O, K       2) N, M       3) K, S       4) M, N       5) P, N

Sol. : Clearly, the given series consist of alternate letters in a reverse order. The alphabets are skipped one at a time. So, the missing terms would be P and N. Ans. (5)

### (a)MIXED SERIES

#### Series Consisting of Letters & Numbers::

Directions (1 – 3): Study the following arrangement carefully and answer the questions given below:

W  1  5  E  J  R  2  M  A  9  T  K  U  N  4  B  I  8  D  H  3  F  6  P  Z  7  Q

Ex. 1. How many such consonants are there, each of which is immediately preceded by a number and immediately followed by a vowel?

(1) None       (2) One       (3) Two       (4) Three       (5) More than three

#### Series Consisting of Letters, Numbers & Symbols

In order to make series more complicated, letters and numbers are combined with different symbols. Consider the following examples:

Directions (4 –6): Study the following arrangement carefully and answer the questions given below :

K  P  5   #  7   M  N  E  2  D  A  ¶  4   F   H  I  T   9  1  \$   U   6%   W   3

Ex. 2: How many such vowels are there in the above arrangement, each of which is either immediately preceded by a number or immediately followed by a symbol?

(1) None       (2) One      (3) Two       (4) Three       (5) More than three

Ans.

### (b)JUMBLED SERIES

Ex. 1. How many such 6 s are there in the following number series which are either immediately preceded by 2 or immediately followed by 9?

2  1  6   9   3   6   2   2   6   4   6   3  6   9  5   9   6   4   2   6  7   3   6   1  6   9   8   2   4  6   9   2

(1) Four       (2) Five       (3) Six       (4) Seven       (5) None of these

Ex. 2. How many such Ms are there in the following letter sequence which are immediately preceded by L and also immediately followed by A?

Z  N  A  L  M  Z  A  B  M  Y  Z  M  A  Y  M  A  Z  A  M  B  N  L  M  A Z  Y

(1) Three       (2) One       (3) Four       (4) Two       (5) None of these

From the examples given above it is evident that you are required to count the number of such letter/digit which satisfies certain conditions in the given letter/number sequence. In other words, you are required to count the conditional letter/number in the given letter/number sequence.

Right Approach for Solving Questions Based on Jumbled Series

1. Spot the required letter/number in the given sequence.
2. Observe minutely to the left and right of such letters/numbers to examine whether they satisfy the conditions or not.
3. Finally, count the letters/numbers which satisfy the required conditions.

Thus, in such questions you are required to spot how many times a particular letter/number satisfying the given conditions are repeated in the given series.