NUMBER SERIES | ADVANCED TIPS & TYPES |

                                                        

SOHEL SAHOO:  Hello Everyone,

In this article you would come to some miscellaneous types of series to know the right pattern at right time quickly.By knowing this you would analyze problems rapidly. As a word of caution note that if at a particular point series sharply increases it is multiplication series.

Read also : Number series | Best trick to find out missing number and for odd man out !

26. Fraction-Series:-

As the name suggests that all the numbers are represented in terms of fraction (Numerator/Denominator) .i.e. {p/q} form; where p & q are integers but q≠0.

Note:-

1.     In fraction series the numerator & denominator  separately make  some known basic series .

2.     There is a relationship or special pattern between numerator & denominator .

3.     While finding the pattern try to arrange with the greatest number according to numerator. [Because greatest no. can be expressed in least cases.]

2/5 , 3/10 , 5/26 , 7/50 , ____

SOL:-Here clear observation  concludes that the numerators i.e. 2,3,5,7 … forms the series of prime no.s &next is ‘11’.

Secondly, the relationship of numerator & denominator is as follow:-

50 = 7²+1

(Here the greatest among denominators is 50 & the only possible relation with its numerator 7 is as stated above.)

Proceeding with this property we got, 5 = 2²+1 , 10 = 3²+1 , 26 = 5²+1

So, the next term will be  11²+1=122.

27. Decimal-Series:-

This series is similar(analog) like fraction-series as every fraction can be expressed as decimal form.

Note:-

1.     In Decimal series the no. before decimal point(.) & no. after decimal point(.)  separately make  some known basic series .

2.     There is a relationship or special pattern between the no. before decimal point(.) & no. after decimal point(.)

3.     While finding the pattern try to arrange with the greatest number after decimal point according to the no. before decimal point. [Because greatest no. can be expressed in least cases.]

   1.1 , 2.8 , 4.16 , 7.343 , ____

SOL:-    Observing the no.s before decimal point we have 1,2,4,7…=>1+1=2 ; 2+2=4 ; 4+3=7 ; next is 7+4=11

No.s after decimal point forms a series  such that 1=1² , 8=2³ , 16=4² , 343=7³ (Greatest no. & its relation with no. before decimal point i.e.7).

Next should be 11²=121

Clearly, the required no. is  11.121 .

28. Alternate-Series:-

As the name says it forms two series with alternate(one spacing another) terms as illustrated below. It is often detected by finding two equal no.s at beginning in exams but not necessarily.

2 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ___ , ___

SOL:- We can rewrite the given series to denote series by colouring as below:

2 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ___ , ___

So, clearly first series 2,3,5,7 forms prime series & next term will be 11.

Next series 2,4,6,8 forms even no. series & hence next term is 10.

Required no.s are 11&10 respectively.

29. Arithmetic-Series:-

In this type of series careful observation will let you know that at a specific interval the terms will start increasing & suddenly decrease at a particular point.

Basically, it indicates that the terms make some groups(sets) at that interval. And the first terms generate other terms by some arithmetic operation(i.e. multiplication/Addition/Division/Subtraction).

2,3,5,6 , 3,4,7,12 , 4,5,___,___

SOL:-  Applying the definition & careful judgement concludes that;

    (2,3,5,6 ), (3,4,7,12) ,( 4,5,___, ___ )

  From 1^st group/set 2+3=5 & 2x3=6

Similarly, 3+4=7 & 3x4=12

Hence, 4+5=9 & 4x5=20

30. Image-Series:-

Here after some number of the series we will observe that the next numbers are the Mirror  image(digits are written in opposite order) of the previous no.s.

16,25,36,49,94,63,52,___

SOL:-  Obviously, this forms an image-series as depicted below.

16,25,36,49, |Mirror| 94,63,52,___

The blank place should be filled by 61.

31.Group-Series:-

In this series every number is a group of a specific digit of that number,i.e. pattern of square/cube etc.

111,428, 9327, 16464,_____

Sol:-   Here 111=1² 1 1³

                428= 2² 2 2³

         9327=3² 3 3³

         16464= 4² 4 4³

Hence, next term should be 5² 5 5³ = 255125

32.Product-Series:-

We can check whether a series of this type or not by visualizing the terms only. Because it increases suddenly after a number.

The terms  are in increasing order with greater differences.

 NOTE:-

1.     We should divide greatest no by its previous no.& express it as

Dividend = divisor x quotient+remainder

2.     Here quotient&remainder forms known basic 5 series or their square or cube.

5,12,40,206,____

SOL:-   206 = 40 x 5+6

            40 =12 x 3+4

         12=5 x 2+2

Quotient forms 2,3,5… i.e. prime series . So next term is 7.

Remainder forms 2,4,6.. i.e. even series. So, next term is 8 .

Blank place will be 206 x 7+8=1450.

33. n-Series:-

It is a special type of series which doesn’t fall in any previous categories.

n-series is based on a general pattern which can be found in terms of n(specific number).

NOTE:-

1.     Here take the two biggest number & start compairing with their nearest squares to find out a pattern.

2.     If any pattern is not found then compare with nearer cube&this will be solved.

3.     By seeing some particular no.s you can directly check for n-series as mentioned below.

12,36,150,392,_____

SOL:- Compare 392 & 150 with their nearest square & cube . Write them in a generalized form as below.

392= 400-8=20²-8 (Not any general pattern)

392 = 343+49=7³+7² ≈ n³+n²

150=144+6=12²+ (12/2) ≈ n²+(n/2)

150=125+25=5³+5² ≈ n³+n²

Hence, we get common pattern as n³+n²

For checking 36= 3³+3² & 12= 2³+2²

Here 2,3,5&7 forms prime series & next term i.e. n=11

Blank place will be n³+n²= 11³+11² = 1331+121=1452 (Ans)

NOTE:-

Now we will learn about some numbers that forms a generalized pattern.By knowing these no.s  you can directly  apply n-series with the pattern. No need to memorise these just have a look to attempt quickly.

150=144+6=12²+ (12/2) ≈ n²+(n/2)

150=125+25=5³+5² ≈ n³+n²

36=6² ≈ n²

36=27+9= 3³+3² ≈ n³+n²

36=27+9= 3³+3x3 ≈ n³+3n

100=10² ≈ n²

100=125-25=5³-5² ≈ n³-n²

100=36+64=6²+8² ≈ n²+(n+2)²

 80=81-1=9²-1 ≈ n²-1

80=64+16=8²+2x8 ≈ n²+2n

80=64+16= 4³+4² ≈ n³+n² 

110=100+10=10²+10 ≈ n²+n

110=121-11=11²-11≈ n²-n

110=125-15=5³-3x5 ≈ n³-3n 

120=121-1=11²-1 ≈ n²-1

120=125-5=5³-5 ≈ n³-n

 130=121+9=11²+(11-2) ≈ n³+(n-2)

130=125+5=5³+5 ≈ n³+n

140=144-4=12²-(12/3) ≈ n³-(n/3)

140=125+15=5³+3x5 ≈ n³+3n

18=16+2=4²+(4/2) ≈ n²+(n/2)

18=27-9= 3³-3² ≈ n³-n²

18=27-9=3³-3x3 ≈ n³-3n

Conclusion:-

1.     If 36&140 are written together then it is of n³+3n.

2.     If 36&150 are written together then it is of n³+n².

3.     If 18&100 are written together then it is of n³-n².

4.     If 18&110 are written together then it is of n³-3n.

5.     If 18&150 are written together then it is of n²+(n/2).

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