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6th Class Mathematics Series SERIES

SERIES

Category : 6th Class

Learning Objective

 

  • To identify different types of number series.
  • To find missing numbers of the series.
  • To find wrong numbers of the series.
  • To learn how to complete the 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.

Types of Series are explained in the following chart:

 

In number series, relationship between the terms is of any kind. For example.

(a) Consecutive even numbers

(b) Consecutive odd numbers

(c) Consecutive prime numbers

(d) Square of numbers

(e) Cubes of numbers

(f)   Square root of numbers

(g)  Omission of certain number of letter in any consecutive order

(h) Addition/subtraction/multiplication/ division by some number (For Ex. A.P & G.P) or any other relation.

 

TYPES OF QUESTIONS:

(I) Complete the series

(II) Find missing number of the series

(III) Find wrong number of the series

 

EXAMPLES ON NUMBER SERIES

 

(I) COMPLETE THE SERIES

 

Example 1: 4, 6, 9, 13,....

(a) 17                                     (b) 18               

(c) 19                                     (d) 20

 Sol.        (b)

 [Correct answer  

Example 2: 64, 32, 16, 8, ?

(a) 0                                       (b) 1                 

(c) 2                                       (d) 4

 

Sol.        (d) Each number is half of its previous number.

 

Example 3: 4, 9, 16, 25,...

(a) 32                                     (b) 42                 

(c) 55                                     (d) 36

 

Sol.        (d) Each number is a whole square.

 

Example 4: 2, 6, 12, 20, 30, 42, 56, ...

(a) 60                                     (b) 64              

(c) 70                                     (d) 72

Sol.        (d) 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8, 8 x 9 = 72

 

(II) TO FIND THE MISSING NUMBER OF SERIES:

 

Examples: 79, 87, ?, 89, 83

(a) 80,                                   (b) 81                

(c) 82                                     (d) 88

Sol.        (b)    

Example 6: 37, 41, ?, 47, 53

(a) 42                                     (b) 43                

(c) 46                                     (d) 44

Sol. (b) Consecutive prime numbers.

 

Example 7 : 21, 34, ?, 89, 144

(a) 43                                     (b) 55                

(c) 64                                     (d) 71

Sol.        (b) Each number is the sum of the two preceding numbers.

21 + 34 = 55

34 + 55 = 89

55 + 89 = 144

 

(III) TO FIND THE WRONG TERM IN THE SERIES:

 

EXAMPLES ON ALPHABETIC SERIES:

 

Example 8: Find the wrong term in the following series EG, JL, OQ, TW,..........

(a) EG                                    (b) JL                 

(c) OQ                                   (d) TW

Sol.        (c)    

Example 9: G, H, J, M, ?

(a) R                                       (b) S                 

(c) Q                                      (d) P

Sol.        (c)    

Example 10: BF, CH, ? , HO, LT

(a) EG                                    (b) EK             

(c) CE                                     (d) FJ

Sol.         (b)    

Example 11: DCXW, FEW, HGTS, ?

(a) LKPO                               (b) ABYZ           

(c) JIRQ                                 (d) LMRS

Sol.        (c) JIRQ

   

EXAMPLES ON ALPHA-NUMERIC SERIES

 

Example 12: K 1, M 3, P 5, T 7, ?

(a) Y 9                                    (b) Y 11

(c) V 9                                   (d) v 11

Sol.        (b) Alphabets follow the sequence

   

 

And numbers are increasing by 2

 

Example 13: Find the missing term.

2 Z 5, 7 Y 7, 14 X 9, 23 W 11, 34 V 13, ?

Sol.        First number is the sum of the number of the proceeding term.

 

Middle letter is moving one step backward.

Third number in a term is a series of odd numbers.

\[\therefore \]  6th term = 47 U 15.

 

EXAMPLES ON MIXED SERIES

Example 14: Complete the series Z, L, X, J, V, H, T, F, _, _

(a) D, R                                 (b) R, D                

(c) D, D                 (d) R, R

Sol.        (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.

Next term of (i) series = R, and

Next term of (ii) series = D

 

Example 15: 7, 5, 26, 17, 63, 37, 124, 65,?,?

(a) 101, 215                         (b) 101,101            

(c) 215, 101                         (d) 215, 215

Sol.        (c) The given series consists of two series

(i) 7, 26, 63, 124.....

(ii) 5, 17, 37, 65.....

In the first series,

\[7={{2}^{3}}\,-1,\,\,26\,={{3}^{3}}-1,\,63={{4}^{3}}-1\]

\[124={{5}^{3}}-1,\,\,\therefore \,{{6}^{3}}-1=215\]

and in the second series.

\[5={{2}^{2}}+1,\,\,17={{4}^{2}}+1,\]

                \[37={{6}^{2}}+1,\,65={{8}^{2}}+1\]

                \[\therefore \,\,\,\,{{10}^{2}}+1=101\]

 

EXAMPLES ON LETTER SERIJS

 

Example 16: b a a b – a b a – b b a - -

(a) bbaa                               (b) aaaa               

(c) abab                (d) baba

Sol.        (d) \[b\,a\,a\,b\,\underline{b}\,a\,/\,b\,a\,\underline{a}\,b\,b\,a\,/\,\underline{b}\,\underline{a}\].

 

Example 17: - - a a b – a – a – b a

(a) bbaab                             (b) ababa             

(c) bbabb            (d) aaaba

Sol.        (b) aba/aba/aba/aba.

 

EXAMPLES ON CORRESPONDENCE SERIES

 

Example 18: A_ BAC_D_BCDC

                                 _ 3 _ 2 _ 1 _ 4 ? ? ? ? 

                                d c _ _ b a c b _ _ _ _

(a) 1, 3, 4, 3        (b) 1, 4, 3, 4          

(c) 2, 3, 4, 3        (d) 3, 4, 1, 4

Sol.        (b) Clearly, 2 corresponds to A.

Now, b corresponds to C and 4 corresponds to b. So, 4 corresponds to C.

c corresponds to D and 3 corresponds to c. So, 3 corresponds to D.

                so, the remaining number i.e., 1 corresponds to B.

Thus, BCDC corresponds to 1, 4, 3, 4.

               

Example 19: 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

Sol.        Comparing the positions of the capital letters, numbers and small letters, we find:

a responds to C and 1 corresponds to a. So, a and 1 correspond to C.

b corresponds to A and 2 corresponds to b. So, b and 2 correspond to A.

Also, 4 corresponds to D.

Sa, the remaining number i.e. 3 corresponds to B. So, BCCB corresponds to 3, 1, 1, 3.

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