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# Number Series Shortcut Tricks & Tips

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## Number Series Tricks & Tips

What is Number Series?

Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in that series, we need to observe and find the accurate number to the series of numbers.

### Tips For Number Series

1 ) Try to observe if there are any familiar numbers in the given series.
2 ) Familiar numbers are the numbers which which are easy to identify like primes numbers, perfect squares, cubes.
3 ) If you are unable to find familiar number, Calculate the differences between the numbers and observe the pattern in the differences.
4)  If the differences are growing slowly it might be an addition or subtraction series or If the differences are growing rapidly it might be a square series, cube series, or multiplicative series.
5) If the differences also are not having any pattern then observe every alternate number (ie every 3rd number form a series) for any pattern.
6) The possible cases may be like sum or the average of two consecutive numbers gives 3rd number.
7 )If still you do not find any pattern, it signifies that the series follows a complex pattern. Check for cases like multiplying the number and adding/subtracting a constant number from it to reach the pattern.

### THE BEST WAY TO SOLVE NUMBER SERIES

There is one approach, which helped me a lot to solve these type of questions. Use this extremely useful tool to crack number series questions: RECOGNIZING THE NUMBERS. The trick is to recognize the numbers in the series and proceed accordingly. However, for this to work, you will need to remember some of the very crucial numbers in maths like:-

1.SQUARES OF NUMBERS
2.SQUARE ROOTS OF NUMBERS
3.CUBES OF NUMBERS
4.CUBE ROOTS OF NUMBERS
5.PRIME NUMBERS
6.NUMBERS WITH A LOT OF DIVISORS (E.g. numbers like 24 or 72)
7.ARITHMETIC TABLES

See the numbers of the given series very carefully. If all the numbers are near some perfect squares or cubes, you need to think on lines of squares or cubes of numbers. If you are not able to find any common factors between the numbers, think along the lines of prime numbers. If you see numbers with a lot of common divisors, think about multiplication or division with common factors. Solving this way would surely reduce the permutations you will need to think before getting the right answer. It is also extremely helpful and surely better than randomly guessing the logic.

But remember – start with the logical answer first and then slowly proceed to a difficult level. So, with this trick, there is a very less probability that you actually miss out on something.

Let me discuss one more important thing that you need to know. There is also a chance that the series is not uniform and continuous. Sometimes, two completely different series are mixed in an alternating fashion. The answer might be easy if you solve questions considering only alternate numbers. There is no way of predicting what the person thought about a question. So, keep your mind open to alternate possibilities. You never know which thought might come handy.

Also, don’t hesitate to leave this type of question if you just seem to figure it out. It’s better to focus on the remaining paper as one question might not affect your score a lot.

Just keep practising a lot. The more you practice such questions, the better you get at solving them and recognizing the logic behind the series quickly.

Different types of Number Series

There are some format of series which are given in Exams.

Perfect Square Series:

This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.

Example 1: 441, 484, 529, 576?

Answer: 441 = 212, 484 = 222, 529 = 232, 576 = 24, 625 = 252.

Perfect Cube Series:

This Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series

Example 2: 1331, 1728, 2197, ?

Answer : 113 ,  123 ,  133 ,  143

Geometric Series:

This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.

Example 3: 5, 45, 405, 3645,?

Answer: 5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.

Mixed Series:

This type of series are more than one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule. This mixed series Examples are describes in separately.

Examples 5:  11, 24, 50, 102, 206, ?

11 x 2 = 22 +2 = 24,

24 x 2 = 48 + 2 = 50,

50 x 2 = 100 + 2 = 102,

102 x 2 = 204 + 2 = 206,

206 x 2 = 412 + 2 = 414.

So the missing number is 414.

Example:- 2, 3, 5, 7,11, 13, _ , 19

Solution:-Here the terms of the series are the prime numbers in order.
The prime number after 13 is 17. So the answer to this question is 17.

Example:-  2, 5, 11, 17, 23, _, 41

Solution:- Here the series is framed by taking the alternative prime numbers. After 23, the prime numbers are 29 and 31. So the answer is 31.

Example:-  3, 5, 8, 13, 21
Solution:- Here starting from third number
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
So, the answer is 13 + 21=34

Example:- 1, 2, 2, 4, 8, 32. _
Solution:- Here starting from the third number
1 X 2 = 2
2 X 2 = 4
2 X 4 = 8
4 X 8 = 32
So, the answer is 8 X 32 = 256

Example:- 4, 7, 10, 13, 16, 19, _, 25
Solution:-Here the difference of any term from its succeding term is 3.
7 – 4 = 3
10 – 7 = 3
So, the answer is 19 +3 =22

Example:-  2, 10, 26, 50, 82, _
Solution:-Here, The difference between two consecutive terms are
10 – 2 = 8
26 – 10 = 16
50 – 26 = 24
82 – 50 = 32
Here, the difference is increased by 8 (or you can say the multiples of 8). So the next difference will be 40 (32 + 8). So, the answer is 82 + 40 =122

Example:-  6, 17, 38, 79, _
Solution:- 6 x 2 + 5 = 17
17 x 2 + 4 = 38
38 x 2 + 3 = 79
So, the answer is 79 x 2 + 2 = 160

Example:- 3, 7, 23, 95, _
Solution:-
3 x 2 + 1 = 7
7 x 3 + 2 = 23
23 x 4 + 3 = 95
So, the answer will be 95 x 5 + 4 = 479

# Practice Set On Number Series

Directions(1-5): Find the missing number in the following number series.

1. 20     24     33    49     74     ?
A) 115
B) 88
C) 96
D) 110
E) 123

Option D
Solution:
20 + 2^2 = 24

24 + 3^2 = 24
33 + 4^2 = 49
49 + 5^2 = 74
74 + 6^2 = 110

2. 1     ?     27    64     125
A) 8
B) 11
C) 12
D) 16
E) None of these

Option A
Solution:
1  = 1^3

? = 2^3 = 8
3 = 3^3
4 = 4^3
5 = 5^3

3. 12   14    17    13   ?   14   21    13
A) 11
B) 8
C) 10
D) 12
E) None of these

Option B
Solution:

12…..(+2)……14….(+3)…..17…..
(-4)……13……(-5)……8……(+6)……14……(+7)…..21…..(-8)…..13
+2, +3, -4, -5, +6, +7, -8

4. 5    11     ?      55      117
A) 22
B) 25
C) 33
D) 30
E) None of these

Option B
Solution:
5  * 2 + 1 = 11
11 * 2 + 3 = 25
25 * 2 + 5 = 55
55 * 2 + 7 = 117

5. 85     43    44    67.5     ?     345
A) 125
B) 140
C) 137
D) 112
E) None of these

Option C
Solution:
85 * 0.5 + 0.5 = 43

43 * 1 + 1 = 44
44 * 1.5 + 1.5 = 67.5
? = 67.5 * 2  + 2 = 137
137 * 2.5 + 2.5 = 345

Directions(6-10): In each of the following questions number series, there is a wrong number that does not follow the pattern of the series. Find the wrong number.

1. 62    87    187    420    812    1437
A) 87
B) 187
C) 420
D) 812
E) None of these

Option C
Solution:
62 + 5^2 = 62 + 25 = 87

87 + 10^2 = 87 + 100 = 187
187 + 15^2 = 187 + 225 = 412
412 + 20^2 = 412 + 400 = 812
812 + 25^2 = 812 + 625 = 1437

2. 120    137    170    222    290   375
A) 137
B) 170
C) 222
D) 290
E) 375

Option B
Solution:
120 + 1 * 17 = 137

137 + 2 *17 = 171
171 + 3 * 17 = 222
222 + 4 * 17 = 290
290 + 5 * 17 = 375

3. 550   542   537   521    496   460
A) 496
B) 521
C) 537
D) 542
E) 460

Option D
Solution:
550 – 2^2 = 546

546 – 3^2 = 537
537 – 4^2 = 521
521 – 5^2 = 496
496 – 6^2 = 460

4. 12      48     168     500    1260   2520
A) 500
B) 168
C) 48
D) 1260
E) 2520

Option A
Solution:
12 * 4 = 48

48 * 3.5 = 168
168 * 3 = 504
504 * 2.5 = 1260
1260 * 2 = 2520

5. 24   536   487    703     670    742
A) 536
B) 487
C) 670
D) 703
E)742

Option C
Solution:
24 + 8^3 = 536

536  – 7^2 = 487
487 + 6^3 = 703
703 – 5^2 = 678
678 + 4^3 = 742

Directions(1-5): In the following number series only one number is wrong. Find out the wrong number.

1. 484   240      118       57        5      11.25     3.625
A) 26.5
B) 57
C) 5
D) 3.625
E) 240

Option  C
Solution:
(484 / 2) – 2 = 240

(240/2) – 2 = 118
(118/2) – 2 = 57
(57/2) – 2 = 26.5
2. 5    7     16     57    244     1245     7506
A) 7506
B) 5
C)244
D) 7
E) 16

Option D
Solution:
5*1 + 1^2 = 6

6*2 + 2^2 = 16
16*3 + 3^2 = 57
57*4 + 4^2 = 244
244*5 + 5^2 = 1245
3. 4     2.5     3.5     6.5     15.5      41.25       126.75
A) 41.25
B) 6.5
C) 126.75
D) 4
E) 2.5

Option B
Solution:
4*0.5 + 0.5 = 2.5

2.5*1 + 1 = 3.5
3.5*1.5 +1.5 = 6.75
6.75*2 + 2 = 15.5
15.5*2.5 + 2.5  = 41.25
41.25*3 + 3 = 126.75
4. 210    209    211    186    202     77
A) 209
B) 77
C) 211
D) 186
E) 202

Option C
Solution:
210 – 1^3 = 209

209 + 2^3 = 213
213 – 3^3 = 186
186 + 4^3 = 202
202 – 5^3 = 77
5. 33       321       465       537        575      591     600
A) 465
B) 33
C) 600
D) 575
E) 591

Option D
Solution:
33 + 288 = 321

321 + 144 = 465
465 + 72 = 537
537 + 36 = 573
573 +18 = 591
591 + 9 = 600

Directions(6-10): What should  come in place of question mark in the following series.

6. 3    7     18    26    ?    53   64   96
A) 37
B) 30
C) 40
D) 35
E) 32

Option A
Solution:
3 + 4  * 2^0 = 7

7 + 11  = 18
18 + 4*(2)^1 = 26
26+ 11 = 37
37 + 4*(2)^2 = 53
53 + 11 = 64
64+ 4 *(2)^3 = 96
7. 1.7     3.2      2.7     4.2     3.7     ?     4.7      6.2
A) 3.8
B) 5.2
C) 4.4
D) 4.8
E) 5.5

Option B
Solution:
1.7    + 1.5 = 3.2

3.2  – 0.5 = 2.7
2.7 + 1.5 = 4.2
4.2 – 0.5 = 3.7
3.7 + 1.5 = 5.2
5.2 – 0.5 = 4.7
4.7 + 1.5 = 6.2
8. 6        8      10     42       ?       770     4578
A) 110
B) 150
C) 132
D) 148
E) 115

Option D
Solution:
6 * 1 + 1*2 = 8

8*2  – 2*3 = 10
10 * 3 + 3*4 = 42
42*4 – 4*5 = 148
148*5 + 5*6 = 770
770*6 – 6*7 = 4578
9. 7    13     31     85      247     ?
A) 733
B) 680
C)700
D) 650
E) 666

Option A
Solution:
7 + 6 = 13

13 + 3 *6 = 31
31 + 3 *18 = 85
85 + 3 * 54 = 247
247 + 3 * 162 = 733
10. 949   189.8     ?     22.776    11.388    6.8328
A) 39.98
B) 40.15
C) 48.53
D) 56.94
E) 55.55

Option D
Solution:
949  * 0.2 = 189.5

189.5 * 0.3 = 56.94
56.94 * 0.4 = 22.778
22.778 * 0.5 = 11.388
11.388 * 0.6 = 6.8328

Directions(1-5): What will come in place of question mark in the given number series.

1. 17 9      15     40      5       ?
A) 620
B) 650.25
C) 550.5
D) 688
E) 540.15

Option  B
Solution:
17 * 0.5 + 0.5 = 9

9 * 1.5 + 1.5 = 15
15 * 2.5 + 2.5 = 40
40 * 3.5 + 3.5 = 143.5
143.5 * 4.5 + 4.5 = 650.25
2. 2     9     25      82      335      ?
A) 1456
B) 1246
C) 1682
D) 1560
E) 1550

Option C
Solution:
2 * 1 + 7 = 9

9 * 2 + 7 = 25
25 * 3 + 7 = 82
82 * 4 + 7 = 335
335 * 5 + 7 = 1682
3. 1548      516     129     43     ?
A) 9.82
B) 11.11
C)13.25
D)10.75
E) 11.25

Option D
Solution:
1548/ 3   = 516

516/4 = 129
129/3 = 43
43/4 = 10.75
4. 41      164       2624       ?        6045696
A)94464
B) 84500
C)94502
D) 78542
E) 82456

Option B
Solution:
41  *   2^2 = 164

164  *  4^2 = 2624
2624  *  6^2 = 94464
94464  *  7^2 = 6045696
5. 4       9       29       119       599        ?
A) 2998
B) 4578
C) 3245
D) 2000
E) 3599

Option E
Solution:
4 * 2 + 1 = 9

9*3  + 2 = 29
29 * 4 + 3 = 119
119* 5 + 4 = 599
599*6 +5=3599

Directions(6-10): In the  following number series only one number is wrong. Find the wrong number.

6. 133     183     241      307     381      463     480
A) 307
B) 133
C) 480
D) 241
E) 381

Option  C
Solution:
133 + 50 = 183

183 + 58 = 241
241 + 66 = 307
307 + 74 = 381
381 + 82 = 463
463 + 90 = 553
7. 31     15      21    50    155.3      767.25
A) 767.25
B) 155.3
C) 15
D) 31
E) 50

Option B
Solution:
31 * 0.5 – 0.5 = 15

15 * 1.5 – 1.5 = 21
21 * 2.5 – 2.5 = 50
50 * 3.5 – 3.5 = 171.5
171.5  *  4.5 – 4.5 = 767.25
8. 18       119      708       3530       14136      42405
A) 14136
B) 708
C) 119
D) 3530
E) 42405

Option D
Solution:
18 * 7 – 7 = 119

119* 6 – 6 = 708
708 * 5 – 5 = 3540
3540 * 4 – 4 = 14136
14136 * 3 – 3 = 42405
9. 500     484     451      384      260      80
A) 80
B) 260
C) 451
D) 484
E) 500

Option B
Solution:
500 – 16 = 484

484 – 33(= 16 + 17) = 451
451 – 67(= 33 + 2 * 17) = 384
384 – 118(= 67 + 3 * 17)= 266
266 – 186(= 118 + 4 * 17)= 80
10. 9    10.8    18     21.6     36      64.8
A) 21.6
B) 10.8
C) 36
D) 18
E) 9

Option D
Solution:
9 + 1.8 = 10.8

10.8 + 2* 1.8 = 14.4
14.4 + 2 *3.6 = 21.6
21.6 + 2*7.2 = 36
36+ 2 * 14.4 = 64.8

Directions (1-5): In the following number series, a wrong number is given. Find out that wrong number.
Q1. 2  11  38  197  1172  8227  65806
(a) 11
(b) 38
(c) 197
(d) 1172
(e) 8227

Q2. 16  19  21  30  46  71  107
(a) 19
(b) 21
(c) 30
(d) 46
(e) 71

Q3. 7  9  16  25  41  68  107  173
(a) 107
(b) 16
(c) 41
(d) 68
(e) 25

Q4. 4  2  3.5  7.5  26.25  118.125
(a) 118.125
(b) 26.25
(c) 3.5
(d) 2
(e) 7.5

Q5. 16  4  2  1.5  1.75  1.875
(a) 1.875
(b) 1.75
(c) 1.5
(d) 2
(e) 4

Directions (6-10) : 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.
Q6. 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

Q7. 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

Q8. 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

Q9. 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

Q10. 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 (11-15) : What should come in place of question mark (?) in the following number series ?
Q11. 13  14  30  93  376  1885  ?
(a) 10818
(b) 10316
(c) 11316
(d) 11318
(e) None of these

Q12. 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

Q13. 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

Q14. 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

Q15. 705  728  774  843  935  1050  ?
(a) 1190
(b) 1180
(c) 1185
(d) 1187
(e) None of these

SOLUTION:

S1. Ans.(d)
Sol. The series is based on the following pattern:
11 = 2 × 3 + 5
38 = 11 × 4 – 6
197 = 38 × 5 + 7
1172 ≠ 197 × 6 – 8
1172 is wrong and it should be replaced by 197 × 6 – 8 = 1174

S2. Ans.(a)
Sol. The series is based on the following pattern:
107 – 71 = 36
71 – 46 = 25
46 – 30 = 16
30 – 21 = 9
21 – 19 = 2≠4
19  should be replaced by 17 for which 21 – 17 = 4

S3. Ans.(d)
Sol. The series is based on the following pattern:
16 = 9 + 7
25 = 16 + 9
41 = 25 + 16
68 ≠ 41 + 25
68 should be replaced by 66.

S4. Ans.(c)
Sol. The series is based on the following pattern: ×0.5,×1.5,×2.5,×3.5,×4.5
Obviously, 3.5 Is the wrong number which should be replaced by 3.

S5. Ans.(b)
Sol. The series is based on the following pattern: ×0.25,×0.5,×0.75,×1,×1.25
Obviously, 1.75 is the wrong number which should be replaced by 1.5.

S6. Ans.(b)
Sol. 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).

S7. Ans.(a)
Sol. The given series is based on the following pattern
13 = 4 × 1 + 1 × 9
40 = 13 × 2 + 2 × 7
135 = 40 × 3 + 3 × 5
552 = 135 × 4 + 4 × 3
2765 = 552 × 5 + 5 × 1
Similarly,
(a) = 2 × l + 1 × 9 = 11
(b) = 11 × 2 + 2 × 7 = 36
(c) = 36 × 3 + 3 × 5 = 123
Hence, 123 will come in place of (c).

S8. Ans.(c)
Sol. The given series is based on the following pattern: ×2+2,÷2-2,×2+2,÷2-2………..
Hence, 4 will come in place of (d).

S9. Ans.(d)
Sol. The given series is based on the following pattern : ×2+7,×2+11,×2+13,×2+17,×2+19
(7, 11, 13, 17, 19, ….. are consecutive prime numbers)
Hence, 159 will come in place of (d).

S10. Ans.(c)
Sol. The given series is based on the following pattern : ×0.5,×1.5,×2.5…….
Hence, 22.5 will come in place of (c).

S11. Ans.(c)
Sol. The given number series is based on the following pattern :
13 × 1 + 1 = 14
14 × 2 + 2 = 30
30 × 3 + 3 = 93
93 × 4 + 4 = 376
376 × 5 + 5 = 1885
? = 1885 × 6 + 6 = 11316
Hence, number 11316 will replace the question mark.

S12. Ans.(b))
Sol. The given series is based on the following pattern :×1.5,×1.5,……..

S13. Ans.(d)
Sol. The given series is based on the following pattern : ×0.6,×0.6……..

S14. Ans.(a)
Sol. The given series is based on the following pattern : ×0.5,×1,×1.5,×2,×2.5…….

S15. Ans.(e)
Sol.
705 + 1 × 23 = 728
728 + 2 × 23 = 774
774 + 3 × 23 = 843
843 + 4 × 23 = 935
935 + 5 × 23 = 1050
? = 1050 + 6 × 23 = 1050 + 138 = 1188

Directions (Q.1-5): What will come in place of the question mark (?) in the following number series?
Q1. 1401, 1402, 705, ?, 77
(a) 243
(b) 242
(c) 244
(d) 246
(e) None of these

Q2. 10, 6, 12, 35, ?, 591.75
(a) 130
(b) 129.5
(c) 127.25
(d) 133
(e) None of these

Q3. 390, 198, ?, 54, 30, 18
(a) 102
(b) 100
(c) 98
(d) 96
(e) None of these

Q4. 10, 77, 474, ?, 9556, 28683
(a) 2275
(b) 2465
(c) 2195
(d) 2385
(e) None of these

Q5. 150, 50, 131, 67, 116, ?, 105
(a) 92
(b) 87
(c) 120
(d) 90
(e) None of these

Directions (Q.6-10): In each of these number series one number is wrong. Find out the wrong number.
Q6. 5, 6, 7.5, 9.75, 13.25, 18.4275
(a) 13.25
(b) 9.75
(c) 18.4275
(d) 7.5
(e) None of these

Q7. 13, 25, 41, 62, 85, 113
(a) 62
(b) 25
(c) 113
(d) 85
(e) None of these

Q8. 250, 55, 16, 8.2, 6.1, 6.328
(a) 6.328
(b) 55
(c) 8.2
(d) 6.1
(e) 16

Q9.  18, 54, 162, 491, 1466
(a) 18
(b) 491
(c) 1466
(d) 54
(e) 162

Q10. 7, 8, 24, 106, 361, 986
(a) 81
(b) 106
(c) 304
(d) 24
(e) None of these

Directions (Q.11-15): In each of these questions, a number series is given. Below the series one number is given followed by (a), (b), (c), (d) and (e) You have to complete this series following the same logic as in the original series and answer the question that follows.

Q11. 5, 9, 25, 91, 414, 2282.5
3 (a) (b) (c) (d) (e)
What will come in place of (c) ?
(a) 63.25
(b) 63.75
(c) 64.25
(d) 64.75
(e) None of these

Q12. 15, 9, 8, 12, 36, 170
19 (a) (b) (c) (d) (e)
What will come in place of (b) ?
(a) 18
(b) 16
(c) 22
(d) 24
(e) None of these

Q13. 7, 6, 10, 27, 104, 515
9 (a) (b) (c) (d) (e)
What will come in place of (d) ?
(a) 152
(b) 156
(c) 108
(d) 112
(e)  None of these

Q14. 6, 16, 57, 244, 1245, 7506
4 (a) (b) (c) (d) (e)
What will come in place of (d) ?
(a) 985
(b) 980
(c) 1004
(d) 1015
(e) None of these

Q15. 8, 9, 20, 63, 256, 1285
5 (a) (b) (c) (d) (e)
What will come in place of (e)
(a) 945
(b) 895
(c) 925
(d) 845
(e) None of these

Solutions

S6. Ans.(a)
Sol.
The pattern of the series is:
×1.2,×1.25,×1.3,×1.35,×1.4,×1.45……….

S7. Ans.(a)
Sol.
The pattern of series is:
+12,+16,+20,+24,+28

S8. Ans.(d)
Sol.
The series is:
÷5+5,÷5+5,÷5+5,÷5+5…….

S9. Ans.(d)
Sol.
The pattern of series is:
×3+1,×3-3,×3+5,×3-7,×3+9……

S11. Ans.(d)
Sol.
The pattern of the given series is :
5 × 1.5 + 1.5 = 7.5 + 1.5 = 9
9 × 2.5 + 2.5 = 22.5 + 2.5 = 25
25 × 3.5 + 3.5 = 87.5 + 3.5 = 91
91 × 4.5 + 4.5 = 409.5 + 4.5 = 414
Similarly,
(a)  3 × 1.5 + 1.5 = 4.5 + 1.5 = 6
(b)  6 × 2.5 + 2.5 = 15 + 2.5 = 17.5
(c)  17.5 × 3.5 + 3.5 = 61.25 + 3.5 = 64.75

S12. Ans.(b)
Sol.
The pattern of the given series is :
15 × 1 – 1 × 6 = 15 – 6 = 9
9 × 2 – 2 × 5 = 18 – 10 = 8
8 × 3 – 3 × 4 = 24 – 12 = 12
12 × 4 – 4 × 3 = 48 – 12 = 36
36 × 5 – 5 × 2 = 180 – 10 = 170
Similarly,
(a)  19 × 1 – 1 × 6 = 19 – 6 = 13
(b)  13 × 2 – 2 × 5 = 26 – 10 = 16

S13. Ans.(a)
Sol.
The pattern of the given series is :
7 × 1 – 1 = 6
6 × 2 – 2 = 10
10 × 3 – 3 = 27
27 × 4 – 4 = 104
104 × 5 – 5 = 515
Similarly,
(a)  9 × 1 – 1 = 8
(b)  8 × 2 – 2 =14
(c)  14 × 3 – 3 = 39
(d)  39 × 4 – 4 = 152

S15. Ans.(c)
Sol.
The pattern of the given series is :
8 × 1 + 1 = 9
9 × 2 + 2 = 20
20 × 3 + 3 = 63
63 × 4 + 4 = 256
Similarly,
(a)  5 × 1 + l = 6
(b)  6 × 2 + 2 = 14
(c)  14 × 3 + 3 = 45
(d)  45 × 4 + 4 = 184
(e)  184 × 5 + 5 = 925

• 4, 5, 6, 14, ?, 100.5
1. 32.5
2. 47.5
3. 67.5
4. 37.5
5. 27.5

Explanation :
4 * 1 + 1 = 5
5 * 1.5 – 1.5= 6
6 * 2 + 2 = 14
14 * 2.5 – 2.5 = 32.5
32.5 * 3 + 3 = 100.5
• 8 4 4 8 32 ?
1.354
2.384
3.294
4.234
5.256

Explanation :
8 * 0.5 = 4
4 * 1 = 4
4 * 2 = 8
8 * 4 = 32
32 * 8 = 256
• 2, 2, 7, ?, 87, 342
1.21
2.26
3.23
4.24
5.22

Explanation :
2 + 1² – 1 = 2
2 + 2² + 1= 7
7 + 4² – 1= 22
• 6, 8, 8, 22, ?, 151
1.43
2.42
3.44
4.47
5.48

Explanation :
6 * 1 + 2 = 8
8 * 1.5 – 4 = 8
8 * 2 + 6 = 22
22 * 2.5 – 8 = 47
47 * 3 + 10 = 151
• 4, ?, 14, 40, 88, 170
1.9
2.5
3.6
4.7
5.2

Explanation :
4 + 1² + 1= 6
6 + 3² – 1= 14
14 + 5² + 1= 40……..
• 6, 6, 7, ?, 91, 463
1.33
2.43
3.38
4.25
5.44

Explanation :
6*1 – 1 + 1 = 6
6*2 – 2 – 3 = 7
7*3 – 1 + 5 = 25
• 2, 5, 17, 50, 122, ?
1.252
2.258
3.257
4.225
5.242

Explanation :
2 + 1³ + 2 = 5
5 + 2³ + 4 = 17
17 + 3³ + 6 = 50
50 + 4³ + 8 = 122
• 2, 9, 39, 161, ?, 2613
1.675
2.670
3.665
4.651
5.655

Explanation :
2 * 4 + 1 = 9
9 * 4 + 3 = 39
39 * 4 + 5 = 161
161 * 4 + 7 = 651
651 * 4 + 9 = 2613
• 5, ?, 20, 34, 76, 142
1.4
2.5
3.7
4.8
5.9

Explanation :
5*2 – 2 = 8
8*2 + 4 = 20
20*2 – 6 = 34
• 5, 6, 8, 30, 136, ?
1.645
2.680
3.650
4.690
5.620

Explanation :
5 * 1 + 1 = 6
6 * 2 – 2 = 10
10 * 3 + 3 = 33
33 * 4 – 4 = 128
128 * 5 + 5 = 645

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