NUMBER SERIES

                                          

Sohel Sahoo: Hello Guys,
        In this article we are going to discuss about number series upon which questions are frequently set in exams. The number series consists of a sequence of numbers in which the next term is obtained by algebraic operation(Addition/subtraction/multiplication/division/square/cube etc.) with the constant terms to the previous term or in that series numbers are arranged in  a certain order.

In number system some numbers are placed wrongly in the series and some numbers are missing 

in exams.You should have proper strategy to deal with them as explained below.

To help you to understand the basic concept & to solve number series problems I have categorized them with respect to certain properties by virtue of which you can crack any type of question in exam.
5 BASIC SERIES:-
We have 5 basic series upon which questions are set in exam. Mainly in acronym square and cube of these  5 series can be represented as [N/E/O/P/NP] or (N/E/O/P/NP)² or (N/E/O/P/NP)³

1. NATURAL NO.S :(N)

1 , 2 , 3 , 4 , 5  ....

2. EVEN NO.S: (E)

2 , 4 , 6 , 8 , 10....

3. ODD NO.S:- (O)

 1 , 3 , 5 , 7 , 9.....

4.PRIME NO.S:- (P)

 2 , 3 , 5 , 7 , 11....

 5. NON-PRIME NO.S: (NP)

 1 ,4 , 6 , 8, 9 ….

In order to master the concept & to solve any type regarding series you have to know square of numbers from 1 to 50 . To find the square of any number you can also check out my article : Mentally square of any number quickly in 2 sec | Vedic math tricks | Full proof

You should know cube of certain numbers especially from 1 to 15.For your kind consideration I have given below.

NUMBER(X)	CUBE(X3)	NUMBER(X)	CUBE(X3)
1	1	9	729
2	8	10	1000
3	27	11	1331
4	64	12	1728
5	125	13	2197
6	216	14	2744
7	343	15	3375
8	512	16	4096

PRIME NUMBERS:-

Defⁿ:-  Any Positive integer (p) greater than 1(P>1) whose only two positive divisiors are 1&P itself is called as a prime number.

ü From 1 to 50 there are 15 prime numbers.viz:-

2,3,5,7,11,13,17,19,23,29,31,37,41,43&47.

ü From 51 to 100 we have 10 more primes;they are as follows:-

53,59,61,67,71,73,79,83,89&97.

Ø That’s why from 1 to 100 there are 25 prime no.s.

v 21 prime numbers are there from 101 to 200 such as:-

101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179, 181,191,193,197&199.

(N/E/O/P/NP)²:-

6. Square of Natural no.s(N²)

    1,4,9,16,25  => 1²,2²,3²,4², so next blank space should be filled up by 5²=25.

7. Square of Even no.s(E²)

    4,16,36,64, 100  => 2²,4²,6²,8², so next blank space should be filled up by 10²=100.

8. Square of Odd no.s(O²)

     1,9,25,49,81  => 1²,3²,5²,7², so next blank space should be filled up by 9²=81.

9. Square of Prime no.s(P²)

    4,9,25,49,121  => 2²,3²,5²,7², so next blank space should be filled up by 11²=121.

10. Square of Non-Prime no.s(NP²)

  1,16,36,64,81  => 1²,4²,6²,8², so next blank space should be filled up by 9²=81.

NOTE:-   

1)    If {3,5,7} appears after 1 then it comprises an odd number series and if {3,5,7} appears after 2 then it continues a series of prime numbers.

2)    If {4,6,8} appears after 2 then it comprises an  Even number series and if {4,6,8} appears after 1 then it continues a series of Non-prime numbers.

(N/E/O/P/NP)³:-

11. Cube of Natural no.s(N³)

    1,8,27,64,125  => 1³,2³,3³,4³, so next blank space should be filled up by 5³=125.

12.Cube of Even no.s(E³)

     8,64,216,512, 1000  => 2³,4³,6³,8³, so next blank space should be filled up by 10³=1000.

13. Cube of Odd no.s(O³)

       1,27,125,343,729  => 1³,3³,5³,7³, so next blank space should be filled up by 9³=729.

14. Cube of Prime no.s(P³)

      8,27,125,343,1331  => 2³,3³,5³,7³, so next blank space should be filled up by 11³=1331.

15. Cube of Non-Prime no.s(NP³)

  1,64,216,512,729  => 1³,4³,6³,8³, so next blank space should be filled up by 9³=729.

DIFFERENCE  SERIES:-

As the name itself suggests that the difference of terms in a  given series will be a special pattern as categorized below which we have studied yet or more to come ahead.

16.(N/E/O/P/NP)

10,12,15,20,27,___

Sol:- Taking difference of terms we have;

(12-10);(15-12);(20-15);(27-20)

ð 2,3,5,7… clearly it forms prime series.

So, next term should be 11 & the blank place would be 27+11 = 38.

17.(N/E/O/P/NP)²

10,14,30,66,130,___

Sol:-Taking difference of adjacent(close to each other)  terms we got series as:

4,16,36,64,…

ð 2²,4²,6²,8² which is a series of square of even no.s

So, next term is 10²=100 & final blank space no. will be 130+100=230.

18.(N/E/O/P/NP)³

10,11,38,163,506,___

Sol:- Clearly the difference gives a new series as :

1,27,125,343 => 1³,3³,5³,7³  forms cube of odd no.s

The next number in the series is 9³=729

Hence blank place no. will be 506+729 = 1235.

19.Constant difference series:-

As per the name difference should be some constant.

10,25,50,65,90,___

Sol:-The difference of terms are as below;

15,25,15,25 [15&25 are 2 constants and appears alternatively here]

So, the next term of difference is 15 & the blank space should be 90+15=105.

20.Double difference series:-

In this type we have to take the difference twice. That means we can’t find any clue on 1^st difference. So, we have to take again difference of 1^st difference.

20,43,70,106,167,___

Sol:-1^st difference gives 23,27,36,61,….

2^nd difference gives 4,9,25, => 2²,3²,5² square of primes.

Next term in 2^nd is 7²=49

So,1^st difference blank place will be 61+49=110.

Hence actual blank place will be 167+110 = 277.

21. Pattern difference series:-

In this type the difference of terms will create some unique pattern from above all difference series types. May be it form multiplication table[2x1=2,2x2=4,2x3=6…]/powers of any constant number(2¹,2²,2³…) etc.

10,18,34,58,90,___

Sol:- Taking differences here we have 8,16,24,32 => multiplication table of 8

Next term should be 8 x 5 =40

Hence blank place answer will be 90+40=130.

22.Addition series:-

It suggest us to continuously add the terms to get next term in the series.

1,2,3,5,8,___

Clearly we have, (1+2=3);(2+3=5);(3+5=8)

So, next will be 5+8=13.

23.Subtraction series:-

It suggest us to continuously subtract the terms to get next term in the series.

13,8,5,3,2,__

Clearly we have, (13-8=5);(8-5=3);(5-3=2)

So, next will be 3-2=1.

24.Multiplication series:-

It suggest us to continuously multiply  the terms to get next term in the series.

2,2,4,8,32,___

Clearly we have, (2x2=4);(2x4=8);(4x8=32)

So, next will be 8x32=256.

25. Division series:-

It suggest us to continuously divide  the terms to get next term in the series.

256,32,8,4,2,___

Clearly we have, (256÷32=8);(32÷8=4);(8÷4=2)

So, next will be 4÷2=2.

Hope, this concept help you to build your concept of solving series.You have to concentrate your mind to visualize the pattern behind it.In the next article I will cover all important types of number series,till then stay tuned& enjoy  reading it over & over.