# How to Solve Number Series Problems in Maths: Tips & Tricks

How to Solve Number Series
Dear Students, minimum 5 questions of Number Series Questions always ask in most of the Bank , SSC and Other Examinations. If you know the shortcuts to solve these number series problems then it can be solved easily. It takes less time to answer. Its scoring topics in Quantitative Aptitude. Hence, Its very important to understand shortcuts and some basic ideas to solve these questions quickly.

ShortCuts#01. Number Series Pattern Based on Whole Number Series:
Pattern::01:: Simple Whole Number Series
Whole Number is: 0,1,2,3,4,5,......
Example: 0, 1, 2, 3, 4, 5, 6, ?
Solution: Since, its a whole number series, so ?=7
Pattern::02:: Square of Whole Number Series
Example: 0, 1, 4, 9, 16, 25, 36, ?
Solution: Since, its a square of whole number series, so ?=7*7=49
Pattern::03:: Cube of Whole Number Series
Example: 0, 1, 8, 27, ?
Solution: Since, its a cube of whole number series, so ?=4*4*4=64
Pattern::04:: nth power of Whole Number Series
Example(Let n=5): 0, 1, 32, ?
Solution: Since, its a 5th power of whole number series, so ?=3*3*3*3*3=243

ShortCuts#02. Number Series Pattern Based on Natural Number Series:
Pattern::01:: Simple Natural Number Series
Natural Number is: 1,2,3,4,5,......
Example: 1, 2, 3, 4, 5, 6, ?
Solution: Since, its a natural number series, so ?=7
Pattern::02:: Square of Natural Number Series
Example: 1, 4, 9, 16, 25, 36, ?
Solution: Since, its a square of natural number series, so ?=7*7=49
Pattern::03:: Cube of Natural Number Series
Example: 1, 8, 27, ?
Solution: Since, its a cube of natural number series, so ?=4*4*4=64
Pattern::04:: nth power of Natural Number Series
Example(Let n=5): 1, 32, ?
Solution: Since, its a 5th power of natural number series, so ?=3*3*3*3*3=243

ShortCuts#03. Number Series Pattern Based on Even Number Series:
Pattern::01:: Simple Even Number Series
Even Number is: 2, 4, 6, 8, 10, 12, .........
Example: 2, 4, 6, 8, ?
Solution: Since, its an even number series, so ?=10
Pattern::02:: Square of Even Number Series
Example: 4, 16, 36, 64, ?
Solution: Since, its a square of even number series, so ?=10*10=100
Pattern::03:: Cube of Even Number Series
Example: 8, 64, 216, ?
Solution: Since, its a cube of even number series, so ?=8*8*8=512
Pattern::04:: nth power of Even Number Series
Example(Let n=4): 16,256, 1296, ?
Solution: Since, its a 5th power of even number series, so ?=8*8*8*8=4096

ShortCuts#04. Number Series Pattern Based on Odd Number Series:
Pattern::01:: Simple Odd Number Series
Odd Number is: 1, 3, 5, 7, 9, 11, ...............
Example: 1, 3, 5, 7, ?
Solution: Since, its an odd number series, so ?=9
Pattern::02:: Square of Odd Number Series
Example: 1, 9, 25, 49, 81, ?
Solution: Since, its a square of odd number series, so ?=11*11=121
Pattern::03:: Cube of Odd Number Series
Example: 1, 27, 125, ?
Solution: Since, its a cube of odd number series, so ?=7*7*7=343
Pattern::04:: nth power of Odd Number Series
Example(Let n=5): 1, 243, 3125, 16807, ?
Solution: Since, its a 5th power of odd number series, so ?=9*9*9*9*9=59049

ShortCuts#05. Number Series Pattern Based on Prime Number Series:
Pattern::01:: Simple Prime Number Series
Prime Number is: 2, 3, 5, 7, 11, .............
Example: 2, 3, 5, 7, ?
Solution: Since, its a prime number series, so ?=11
Pattern::02:: Square of Prime Number Series
Example: 4, 9, 25, 49, 121, ?
Solution: Since, its a square of prime number series, so ?=13*13=169
Pattern::03:: Cube of Prime Number Series
Example: 8, 27, 125, ?
Solution: Since, its a cube of prime number series, so ?=7*7*7=343
Pattern::04:: nth power of Prime Number Series
Example(Let n=5): 32, 243, 3125, ?
Solution: Since, its a 5th power of prime number series, so ?=7*7*7*7*7=16807

ShortCuts#06. Number Series Pattern Based on Integer:
Pattern::01:: Simple Integer
Integer is: ..............,-4,-3,-2,-1,0,1,2,3,4,....................
Example: -4,?,-2,-1,0,1,2,3
Solution: Since, its a simple integer series, so ?=-3
Pattern::02:: Square of Integer
Example: 16,?,4,1,0,1,4,9
Solution: Since, its a square of integer, so ?=-3*-3=9
Pattern::03:: Cube of Integer
Example: -64,?,-8,-1,0,1,8,27
Solution: Since, its a cube of integer, so ?=-3*-3*-3=-27
Pattern::04:: nth power of Integer
Example(Let n=5): -1024,?,-32,-1,0,1,32,243
Solution: Since, its a 5th power of integer, so ?=-3*-3*-3*-3*-3=-243

ShortCuts#07. Number Series Based on continuous increasing or decreasing by a specific term :
Pattern::01:: Continuous Increasing
Example: 88, 90, 92, 94, ?
Solution: Since, its a continuous increasing series by +2, so ?=94+2=96
Pattern::01:: Continuous Decreasing
Example: 67, 61, 55, 49, ?
Solution: Since, its a continuous decreasing series by -6, so ?=49-6=43

ShortCuts#08. Number Series Based on continuous product or division by a specific term :
Pattern::01:: Continuous Multiplication/Product
Example: 12.5, 25, 50, 100 200, ?
Solution: Since, its a continuous multiplication series by *2, so ?=200*2=400
Pattern::01:: Continuous Division
Example: 100, 50, 25, ?
Solution: Since, its a continuous division series by 2, so ?=25/2=12.5

ShortCuts#09. Number Series Based on *x+y :
Example: 13, 41, 125, ?
Solution: Since, its pattern is *3+2, so ?=125*3+2=252
[Note: *, +, - and / any two or three or more operations can take place.]

ShortCuts#09. Number Series Based on Combination of two series:
Example: 5, 9, 25, 81, 125, 729, 625, ?
Solution: Since, its the combination of two number series which can be observed:
Series 1: 5, 25, 125, 625
Logic: Each term is multiplied by 5 to get next term.
Series 2: 9, 81, 729, ?
Logic: Each term is multiplied by 9 to get next term, so next term = 729*9 = 6561

ShortCuts#09. Number Series Based on triangular shaped solution :
Example: 15, 15, 23, 55, 135, ?
Solution:

Types of Number Series Ask in the Exams:
1. Missing Number Series:
Example: 1, 3, 5, ?, 9, 11
Solution: Since, its an odd number series, so ?=7
2. Wrong Number Series:
Example: 2, 4, 6, 8, 13, 12
Solution: From the given series it can be observed that it should be an even number series, 13 is placed a wrong number, in place of 13, there should be 10.
3. Next Term Number Series:
Example: 2, 3, 5, 7, ___
Since, Its a prime number series, so next term will be 11.
4. New type of Number Series generally ask in Bank PO Examination:
Example:
3  19  103  439  1381  2887
5  (a)  (b)   (c)     (d)     (e)
What will come in place of (b) ?
Solution: The given series is based on the following pattern : ×6+1,×5+8,×4+27,×3+64,×2+125
Similarly, 5×6+1=31
31×5+8=163
Hence, 163 will come in place of (b).

Solve These Important Number Series Questions asked in Various Competitive Examinations:
Directions (Q1-Q19) : What should come in place of question-mark (?) in the following number series ?
Q1. 8, 7, 13, 38, 151, ?
Q2. 9, 5, 6, 10.5, 23, ?
Q3. 18, 20, 26, 38, ?, 88
Q4. 1, 20, 58, 134, ?, 590
Q5. 2, ?, 256, 1024, 2048, 2048
Q6. 190, 94, 46, 22 ?
Q7. 7, 4, 5, 12, 52, ?
Q8. 6, 4, 5, 11, 39, ?
Q9. 89, 88, 85, 78, 63, ?
Q10. 5, 28, 47, 64, 77, ?
Q11. 7, 3, 2, 2, 4, ?
Q12. 2, 13, 26, 43, 62, ?
Q13. 519, 517, 509, 483, 403, ?
Q14. 27, 38, 51, 68, 87, ?
Q15. 2, 8, 28, 54, 53, ?
Q16. 167, 164, 159, 150, ? , 100
Q17. 17, 31, 15, 33, 13 , ?
Q18. 973, 325 , 109 , 37 , 13 , ?
Q19. 0.5 , 2, 8, 35, ? , 1079
Directions (Q20-Q24): In the following number series, a wrong number is given. Find out that wrong number.
Q20. 2  11  38  197  1172  8227  65806
(a) 11
(b) 38
(c) 197
(d) 1172
(e) 8227
Q21. 16  19  21  30  46  71  107
(a) 19
(b) 21
(c) 30
(d) 46
(e) 71
Q22. 7  9  16  25  41  68  107  173
(a) 107
(b) 16
(c) 41
(d) 68
(e) 25
Q23. 4  2  3.5  7.5  26.25  118.125
(a) 118.125
(b) 26.25
(c) 3.5
(d) 2
(e) 7.5
Q24. 16  4  2  1.5  1.75  1.875
(a) 1.875
(b) 1.75
(c) 1.5
(d) 2
(e) 4
Directions (Q25-Q29) : In each of the following questions a number series is given. After the series a number is given followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the given number, following the sequence of original series and answer the questions that follow the series.
Q25. 3  19  103  439  1381  2887
5  (a)  (b)   (c)     (d)    (e)
What will come in place of (b) ?
(a) 139
(b) 163
(c) 161
(d) 157
(e) None of these
Q26. 4  13  40  135  552  2765
2  (a)  (b)  (c)   (d)    (e)
What will come in place of (c) ?
(a) 123
(b) 133
(c) 127
(d) 131
(e) None of these
Q27. 5  12   4    10    3    8
6  (a) (b)  (c)  (d)  (e)
What will come in place of (d) ?
(a) 3
(b) 5
(c) 4
(d) 7
(e) None of these
Q28. 3  13  37  87  191  401
1  (a)  (b) (c)  (d)   (e)
What will come in place of (d) ?
(a) 169
(b) 161
(c) 171
(d) 159
(e) None of these
Q29. 8    4    6   15  52.5  236.25
12  (a)  (b)  (c)  (d)     (e)
What will come in place of (c) ?
(a) 23.5
(b) 16.5
(c) 22.5
(d) 22.25
(e) None of these
Directions (Q30-Q34) : What should come in place of question-mark (?) in the following number series ?
Q30. 13  14  30  93  376  1885  ?
(a) 10818
(b) 10316
(c) 11316
(d) 11318
(e) None of these
Q31. 4  6  9  13.5  20.25  30.375   ?
(a) 40.25
(b) 45.5625
(c) 42.7525
(d) 48.5625
(e) None of these
Q32. 400  240  144  86.4  51.84  31.104   ?
(a) 19.2466
(b) 17.2244
(c) 16.8824
(d) 18.6624
(e) None of these
Q33. 9  4.5  4.5  6.75  13.5  33.75   ?
(a) 101.25
(b) 103.75
(c) 99.75
(d) 105.50
(e) None of these
Q34. 705  728  774  843  935  1050  ?
(a) 1190
(b) 1180
(c) 1185
(d) 1187
(e) None of these