Series Questions and its all types for banking,ssc and all competitive exams

 

Type-1

Logic based on –Arithmetic  progression

We all are familiar with the term of arithmetic Progression .let us take recap of this concept .

If a series is written like this way  –

a     a + d     a + 2d      a + 3d       a + 4d        a + 5d              -----------------     a +(n-1) d    

first term = a  ,   common difference(d) = next term – previous term   ,        last term = a +( n-1)d  

Example -     4     8     12      16      20      ?      ?

      In this sequence we can easily see when we go from left hand side to right hand side continuously then there is a gape of 4 which is nothing but common difference so .after 20 there will gape of 4 so term will be = 20 + 4 = 24    and 24 +4 = 28 

2^nd example -  1.5       3       4.5     6     7.5    ? 

       In first look always try to solve questions with this common difference logic if it will not work then we will switch on another logic but here , it is working

    Common difference in series =  3- 1.5 = 4.5-3 = 6-4.5 = 7.5-6 = 1.5 = same 

So,  when we go from left to right in series then for getting next term we will only add 1.5 to its previous term so ,

       7.5 + 1.5 = 9 

Tips –In first  look try to use this logic when you see that series is increasing/ decreasing   slowly .

TYPE -2 

LOGIC BASED ON -  INCREASING SERIES / DECREASING SERIES WITH SOME FIXED PATTERN

We can best understand with some good examples –

Increasing series - 

           2          5           9           14            20             27            ? 

     Step-1   3           4           5              6                7                            ----- take common diff.

     Step 2         1            1            1                1             1        7+1=8  so, number=27 +8=35

Note – either we can move from left hand side to right with addition or from right to left with subtraction .it is up to you but better to move from left to right . 

Decreasing series-

Example -    100       97        94        91         88    ?

                            3          3          3             3          88-3 = 85

           Common diff.= 3 

TYPE -3  MULTIPLICATION SERIES

It is one of popular pattern especially asked in banking examinations of any standard i.e., PO level or clerical level. In these days these type of questions have been framed by Tata consultancy service, the most prominent exam taking agency in India so, once you learn here then you will able to crack this type of series easily in any of the competitive exams.

we will understand this by taking one basic example based on multiplication series. multiplications is done for increasing the series.

100         100           150           300          750          ?                ?      

Sol- In first view you see there is no changing in first two initial numbers so, you should think how we can easily bring the second number from the first beginning number , it is simply by multiplying by 1. Similarly think how you will bring third number from second number you will be get multiplying by 1.5.

second number= 100= 100 * 1 

third number(150)= 100 * 1.5  

fourth number (300)= 150 * 2

we are seeing number(multiplication number is increasing by 0.5) 

fifth number (750) = 300 * 2.5 

sixth number (?) = 750 * 3 = 2250

seventh number (?) = 2250 * 3.5=7875

There are some popular questions is being provided here which comes frequently in all competitive exams.

Q1. 8    12     24     60     ? 

Sol-  12 = 8 * 1.5  

Note- At first think how second number we can bring from first number so, 12 can get from 8 by multiplying with 12/8 i.e.,3/2=1.5 .

        24 = 12 *2 

        60= 24 * 2.5

        ?=    60 * 3= 180 

 Q2.  1.5    1.5     2.25    4.50   11.25     ?

     Sol-   1.5 = 1.5 * 1

               2.25 = 1.5 * 1.5

               4.50 = 2.25 * 2

                11.25 = 4.50 * 2.5

                ?    =   11.25 * 3= 33.75.

Q3.  150      150        300          900          3600        ?

Sol-   150 = 150 *1 

          300 = 150 * 2

          900  = 300 *3

         3600 = 900 * 4

          ?      =  3600 * 5 =  180000

Q4. 100    50     50     75         150     ? 

Sol-   50 = 100 * 1/2

          50 = 50 * 1

          75 = 50 * 1.5 

          150 = 75 * 2

           ?    =  150 * 2.5 = 375

Q5. 420    210     140     105      84    ? 

Sol-  210 = 420 * 1/2 

        140 =  210  * 2/3 

          105  = 140  *  3/4

            84=   105 * 4/5 

           ? =  84 * 5/6 = 70  

     TYPE- 4 

Square Series(Square of natural number N^2)- As from its name, it is clear this concept is based upon squaring of a number. To solve quickly , it is very necessary to memorize table from 11 to 30.

Ex-   121      144       169         196           ?          ?    

 Sol-  11 ^2  12^2     13 ^2       14 ^2    15^2    16^2 

so, ? = 225      and another ? = 256 

Table-  Square table from 11 to 30

11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400
21	441
22	484
23	529
24	576
25	625
26	676
27	729
28	784
29	841
30	900

 

TYPE-5  

LOGIC BASED ON -     ( NATURAL NO.)² + 1  

In  this series based questions you will get pattern based on square of natural number + 1. Let us Come we will understand best with some brilliant examples.

Ex1.  2           5           10               17                   26               37           ?

Sol- Whenever during solving question any number is very close to square of natural number you should focus to this pattern. generally the given number will be greater than square of number by 1 but it could be any thing.

 2 = 1^2 + 1 ,  5= 2^2 +1 , 10 = 3 ^2 +1 , 17 = 4^2 +1 , 26 = 5^2+1 , 37 = 6^2 +1  

so next number will be 7^2 +1 = 50   

Tips- Remember table of square which is given in above pattern, it will reduce more time while attempting paper.

TYPE-6 

LOGIC BASED ON- (NATURAL NO.)^2 -  1

EX1.  0      3         8           15         24          ?

       Sol-  0= 1^2-1  ,  3 = 2^2-1 , 8 = 3^2 -1,  15= 4^2 -1  , 24= 5 ^2 -1    similarly ,

next missing number will be = 6^2 -1 = 35