**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 + 6

^{3}– 6 = 328

328 + 7

^{3}– 7 = 664

664 + 8

^{3}– 8 = 1168

1168 + 9

^{3}– 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.

**Related Topic:**

Sequence and Series | Progression | Type of Sequence

Arithmetic Sequences and Series | Arithmetic Mean

Geometric Sequences and Series | Geometric Mean

Harmonic Sequence | Harmonic Mean