### Why this topic is important?

Questions on number series are prevalent in most of the competitive aptitude exams. These questions are based on numerical sequences that follow a logical pattern based on elementary arithmetic concepts. A particular series is given from which the pattern must be analyzed. You are then asked to predict the next number in the sequence following the same rule.
Generally, there are three types of questions asked from the number series:

1. A numerical series is given in which a number is wrongly placed. You are asked to identify that particular wrong number.
2. A numerical series is given in which a specific number is missing. You are required to find out that missing number.
3. A complete numerical series is followed by an incomplete numerical series. You need to solve that incomplete numerical series in the same pattern in which the complete numerical series is given.

### Concept of Number Series

A Number Series is a sequence of numbers obtained by some particular predefined rule and applying the predefined rule it is possible to find out the next term of the series.

A number series can be created in many ways. Some of these are discussed below:

### Arithmetic Series

An arithmetic series is one in which successive numbers are obtained by adding (or subtracting) a fixed number to the previous number.

Example:
(i) 3, 5, 7, 9, 11,…..
(ii) 10, 8, 6, 4, 2,….
(iii) 13, 22, 31, 40, 49,….
(iv) 31, 27, 23, 19, 15,……etc.
These arithmetic series because in each of them the next number can be obtained by adding or subtracting a fixed number. (For example 3,5,7,9….. every successive number is obtained by adding 2 to the previous number).

### Geometric Series

A geometrical series is one in which each successive number is obtained by multiplying (or dividing) a fixed number by the previous number.

Example:
(i) 4, 8, 16, 32, 64,…..
(ii) 15, -30, 60, -120, 240,….
(iii) 1024, 512, 256, 128, 64,….
(iv) 3125, -625, 125, -25, 5,….etc
Are geometric series because, in each of them, the next number can be obtained by multiplying (or dividing) the previous number by a fixed number.( For example: 3125,-625,125,-25,5…. Every successive number is obtained by dividing the previous number by -5).

### Series Of Squares, Cubes etc…:

These series can be formed by squaring or cubing every successive number.

Example:
(i) 2, 4, 16, 256,.….
(ii) 3, 9, 81, 6561,….
(iii) 2, 8, 512,…..etc.
Are such series. ( In the first and second, every number is squared to get the next number while in the third it is cubed.)

### Mixed Series

A mixed series is basically the one we need to have a sound practice of because it is generally the mixed series which is asked in the examination. By a mixed series, we mean a series that is created according to any non-conventional (but logical) rule. Because there is no limitation to people’s imagination, there are infinite ways in which a series can be created and naturally it is not possible to club together all of these mixed series.

Example:
(i) 1, 2, 3, 5, 10, 17, 26, 37,….
(ii) 3, 5, 9, 15, 23, 33,….
Are examples of such series. {In 1,2,5,10,17,26,37,…the difference of successive numbers are 1,3,5,7,9,11,… which is an arithmetic series.}

### Missing Number Series Questions

Problem 1: 78, 56, 84, 62, ? ,68
Solution:
78 – 22 = 56
56 + 28 = 84
84 – 22 = 62
62 + 28 = 90
90 – 22 = 68

Problem 2: 118, 328, 664, 1168, ?
Solution:
118 + 63 – 6 = 328
328 + 73 – 7 = 664
664 + 83 – 8 = 1168
1168 + 93 – 9 = 1888

Problem 3: 8, 50, 295, ? , 5881, 17641
Solution:
8 x 7 – 6 = 50
50 x 6 – 5 = 295
295 x 5 – 4 = 1471
1471 x 4 – 3 = 5881
5881 x 3 – 2 = 17641

Problem 4: 10, 15, 35, 82.5, ? , 562.5
Solution:
10 x 0.5 + 10 = 15
15 x 1 + 20 = 35
35 x 1.5 + 30 = 82.5
82.5 x 2 + 40 = 205
205 x 2.5 + 50 = 562.5

Problem 5: 11,22, 66, ? , 2310, 25410
Solution:
11 * 2 = 22
22 * 3 = 66
66 * 5 = 330
330 * 7 = 2310
2310 * 11 = 25410

Problem 6:1000, 501, 170, 47.5, ?
Solution:
1000 ÷ 2 + 1 = 501
501 ÷ 3 + 3 = 170
170 ÷ 4 + 5 = 47.5
47.5 ÷ 5 + 7 = 16.5

Problem 7: 1290, 645, 430, ? , 258, 215
Solution:
1290 * (1/2) = 645
645 * (2/3) = 430
430 * (3/4) = 322.5
322.5 * (4/5) = 258
258 * (5/6) = 215

Problem 8: 1386, 1386, 693, 231, 57.75, ?
1386 ÷ 1 = 1386
1386 ÷ 2 = 693
693 ÷ 3 = 231
231 ÷ 4 = 57.75
57.75 ÷ 5 = 11.55

Problem 9:75000, 3000, 150, ? , 1, 0.2
Solution:
75000 ÷ 25 = 3000
3000 ÷ 20 = 150
150 ÷ 15 = 10
10 ÷ 10 = 1
1 ÷ 5 = 0.2

Problem 10: 675, 674, 336, 111, 26.75, ?
Solution:
(675 –1)/1 = 674
(674 –2)/2 = 336
(336 –3)/3 = 111
(111 –4)/4 = 26.75
(26.75 –5)/5 = 4.35

Problem 11: 208, 104, 156, 390, ? , 6142.5
Solution:
208 * 0.5 = 104
104 * 1.5 = 156
156 * 2.5 = 390
390 * 3.5 = 1365
1365 * 4.5 = 6142.5

Problem 12: 45, 48, 102, 315, 1272, ?
Solution:
45 * 1 + 3 = 48
48 * 2 + 6 = 102
102 * 3 + 9 = 315
315 * 4 + 12 = 1272
1272 * 5 + 15 =6375

Problem 13: 456, 228, 228, 456, 1824, ?
Solution:
456 * ½ = 228
228 * 1 = 228
228 * 2 = 456
456 * 4 = 1824
1824 * 8 = 14952

Problem 14: 1156, 1159, 1171, 1198, 1246, ?
Solution:
1156 + (1 * 3) = 1159
1159 + (2 * 6) = 1171
1171 + (3 * 9) = 1198
1198 + (4 * 12) = 1246
1246 + (5 * 15) = 1321

Problem 15: 36, 39, 51, ? , 126, 201
Solution:
36 + (1 * 3) = 39
39 + (2 * 6) = 51
51 + (3 * 9) = 78
78 + (4 * 12) = 126
126 + (5 * 15) = 201

### Wrong Series Questions

Problem 1: 22, 24, 32, 70, 168, 511
Solution:
22 * 1 + 2 = 24
24 * 1.5 – 4 = 32
32 * 2 + 6 = 70
70 * 2.5 – 8 = 167
167 * 3 + 10 = 511

Problem 2: 730, 366, 184, 92, 47.5, 24.75
Solution:
730 /2 + 1 = 366
366 /2 + 1 = 184
184 /2 + 1 = 93
93 /2 + 1 = 47.5
47.5 /2 + 1 = 24.75

Problem 3: 8, 8, 40, 360, 4675, 79560
Solution:
8 * 1 = 8
8 * 5 = 40
40 * 9 = 360
360 * 13 = 4680
4680 7 = 79560

Problem 4: 53760, 6720, 960, 160, 80, 8
Solution:
53760/8 = 6720
6720/7 =960
960/6 = 160
160/5 = 32
32/4 = 8

Problem 5: 80, 120, 300, 1040, 4725, 25987.5
Solution:
80 * 1.5 = 120
120 * 2.5 = 300
300 * 3.5 = 1050
1050 * 4.5 = 4725
4725 * 5.5 = 25987.5

Problem 6: 19, 20, 45, 129, 520, 2605
Solution:
19 * 1 + 1 = 20
20 * 2 + 2 = 42
42 * 3 + 3 = 129
129 * 4 + 4 = 520
520 * 5 + 5 = 2605

Problem 7: 42, 86, 348, 2094, 16758
Solution:
42 * 2 + 2 = 86
86 * 4 + 4 = 348
348 * 6 + 6 = 2094
2094 * 8 + 8 =16760

Problem 8: 2592, 1296, 1944, 4860, 17010, 76540
Solution:
2592 * 0.5 = 1296
1296 * 1.5 = 1944
1944 * 2.5 = 4860
4860 * 3.5 = 17010
17010 * 4.5 = 76545

Problem 9: 14, 29, 88,353, 1766, 10598
Solution:
14 * 2 + 1 = 29
29 * 3 + 1 = 88
88 * 4 + 1 = 353
353 * 5 + 1 = 1766
1766 * 6 + 1 = 10597

Problem 10: 53, 26, 27, 39, 80, 197, 595.5
Solution:
53 * 0.5 -0.5 = 26
26 * 1 + 1 = 27
27 * 1.5 –1.5 = 39
39 * 2 + 2 = 80
80 * 2.5 –2.5 = 197.5
197.5 * 3 + 3 = 595.5

Problem 11: 21, 43, 88, 175, 362, 729
Solution:
21 * 2 + 1 = 43
43 * 2 + 2 = 88
88 * 2 + 3 = 179
179 * 2 + 4 = 362
362 * 2 + 5 = 729

Problem 12: 534, 266, 132, 64, 31.5, 14.75
Solution:
534/2 –1 = 266
266/2 –1 = 132
132/2 –1 = 65
65/2 –1 = 31.5
31.5/2 –1 = 14.75

Problem 13 4, 26, 178, 1238, 8672
Solution:
4 * 7 – 2 = 26
26 * 7 – 4 = 178
178 * 7 – 6 =1240
1240 * 7 – 8 = 8672

Problem 14: 2, 26, 286, 2004, 10010, 30030
Solution:
2 * 13 = 26
26 * 11 = 286
286 * 7 = 2002
2002 * 5 = 10010
10010 * 3 = 30030

Problem 15 97, 110, 136, 175, 227, 290
Solution:
97 + (13 * 1) = 110
110 + (13 * 2) = 136
136+ (13 * 3) = 175
175 + (13 * 4) = 227
227 + (13 * 5) = 292

I hope, this article will help you a lot to understand the Number Series Concept And Tricks | Problems. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.