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Series

A series is a sequence of numbers/alphabetical letters or both which follow a particular rule. Each element of series is called 'term'. We have to analyse the pattern and find the missing term or next term to continue the pattern. There are different types of Series which are explained below -

Type - I - Number Series - A series that is made only of number or digit. In number series, relationship between the terms is of any kind. They can be,

i) Consecutive even numbers

ii) Consecutive odd numbers

iii) Consecutive prime numbers

iv) Square of numbers

v) Cubes of numbers

vi) Square root of numbers

vii) Omission of certain number of letter in any consecutive order

viii) Addition/subtraction/multiplication/division by some number.

Example 1 - Which of the following is the next term of series given below ?

4, 6, 9, 13, .....

(a) 17  (b) 18  (c)  19  (d) 20

Solution: b. Difference between any two number in the series is in continuous increasing order, i.e., difference between 6 and 4 is 2, 9 and 6 is 3, 13 and 9 is 4.

Example 2 - What will come in place of question mark in the following series?

79, 87, ?, 89, 83

(a) 80  (b) 81  (c) 82  (d) 88

Solution: b. There is difference of +8 between 79 and 87 and -6 between 89 and 83. Applying both for obtaining the missing number we get 81.

Example 3 - What will come in place of question mark in the following series?

21, 34, ?, 89, 144

(a) 43  (b) 55  (c) 64  (d) 71

Solution: b.  Each number is the sum of the two preceding numbers.

21+34=55, 34+55=89, so on.

Example 4 - Find the wrong term in the series-

3, 8, 15, 24, 34, 48, 63.

(a) 15  (b) 18  (c) 34  (d) 63

Solution: c. 22   - 1, 32 - 1, 42 - 1, 52 - 1 so on.

Type - II - Alphabet Series - Similar to number series it consists of  alphabets only. Series could be made up of single alphabets or series of group of alphabets and each group having some common relationship.

Example - What will come in place of question mark in the following series?

BF, CH, ?, HO, LT

(a) FG  (b) EK  (c) CE  (d) FJ

Solution: b. B - C - E - H - L (there is continuous increase in the gap between alphabets, i.e., 1,2,3,4).  Similarly, F - H - K - O - T (there is continuous increase in the gap between alphabets, i.e., 2,3,4,5).

Type - III - Alpha - Numeric Series - It is a combination of both alphabet and number to create a series.

Example - What will come in place of question mark in the following series?

K1, M3, P5, T7, ?

(a) Y9  (b) Y11  (c) V9  (d) V11

Solution: a. K +2 = M + 3 = P + 4 = T + 5 = Y. Numbers are increasing by 2.

Type - IV -Mixed Series - Mixed series normally consists of two or more  series working within the series.

Example - Complete the series -

Z, L, X, J, V, H, T, F, _, _

(a) D,R  (b) R,D  (c) D,D  (d) R,R

Solution: b. The given sequence consists of two series

i) Z, X, V, T, _

ii) L, J, H, F, _. Both consisting of alternate letters in the reverse order.

Type - V - Letter Series -  A series of letters, which follow a certain pattern, is given with four/five times blank spaces in between. The order of missing letters is correct answer.

Example - Which sequence of letters when placed at the blanks one after another will complete the given letter series?

b a a b _ a b a _ b b a _ _

(a) bbaa  (b) aaaa  (c) abab  (d) baba

Solution: d. b a a b b a / b a a b b a / b  a