## Number Series Part 1

Problem 1: 7   14   30   56   93  ?

Double difference

7 -14 =+7

14 – 30 = +16

30 – 56 = +26

56 – 93 = 37

Second difference

7 – 16 = +9

16 – 26 = +10

26 – 37 = +11

12+37+93 = 142

Problem 2: 11   13   20   111   ?

11 – 13 = 2 = $1^{3}+1$

13 – 20 = 7 = $2^{3}-1$

20 – 48 =28 = $3^{3}+1$

48 – 111 = 63 = $4^{3}-1$

$5^{3}+1=126+111=237$

Problem 3: 42  45   52   65   86   ?

Double difference

42 – 45 = 3

45 – 52 = 7

52 – 65 = 13

65 – 85 = 21

Second difference

3 – 7 = 4

7 – 13 = 6

13 – 21 = 8

10+21+86 = 117

Problem 4: 7   5   7   17   63   ?

7*1 – 2 = 5

5*2 – 3 = 7

7*3 – 4 = 17

14*4 -5 =63

63 * 5 – 6 =309

Problem 5: 13   12   16   7   23   ?

13 -12 = -1 = $1^{2}$

12 – 16 = +4 = $2^{2}$

16 -7 = -9 =$3^{2}$

7 – 23 = +16=$4^{2}$

$5^{2}$=25

23-25 = -2

## Number Series Part 2

Problem 1: 3   9   31   89   175   ?

3 * 5 – 6 = 9

9 * 4 – 5 = 31

31 * 3 – 4=89

89 * 2 – 3=175

175*1 – 2=173

Problem 2: 33   321   465   537   573   ?

321 – 33 = 288

465 – 321=144

537 – 465 = 72

573 – 537 = 36

$\frac{288}{2}=144$     $\frac{144}{2}=72$      $\frac{72}{2}=36$   $\frac{36}{2}=18$

18+573 = 591

Problem 3: 16   8   12   30   ?   472.5

16 * 0.5 = 8

8 * 1.5 = 12

12 * 2.5 = 30

30 * 3.5 = 105

105 * 4.5 = 472.5

Problem 4: 6   3.5   4.5   11   48   ?

6 * 0.5 + 0.5 = 3.5

3.5 * 1 + 1= 4.5

4.5 * 2 + 2 = 11

11 * 4 + 4 = 48

48 * 8 + 8 = 382

Problem 5: 3   4.5   9   22.5   67.5   ?   945

3 * 1.5 = 4.5

4.5 * 2 = 9

9 * 2.5 = 22.5

22.5 * 3 = 67.5

67.5 * 3.5 = 236.25

## Number Series Part 3

Problem 1: 4   6   14   44   ?   892

4 * 1 + 2 = 6

6 * 2 + 2 = 14

14 * 3 + 2 = 44

44 * 4 + 2 = 178

Problem 2: 7   3   2   2   4   ?

7 * 0.5 – 0.5 = 3

3 * 1 -1 = 2

2 * 2 – 2 = 2

2 * 4 – 4 = 4

4 * 8 – 8 = 24

Problem 3: 5   6   14   23   87   ?

5 – 6 = 1 = $1^{2}$

6 – 14 = 8 = $2^{3}$

14 – 23 = 9 = $3^{2}$

87 – 23 = 64 = $4^{3}$

$5^{2}=25$

87+25 = 112

Problem 4: 5   6.2   9   13.4   19.4   ?

5 – 6.2 = 1.2

9 – 6.2 = 2.8

13.4 – 9 = 4.4

Second diference

2.8 – 1.2 = 1.6

4.4 – 2.8 = 1.6

1.6+4.4 = 6

1.6 + 6 + 19.4 = 27

Problem 5: 3   2   2   3   8   35   ?

3 * 1 – 1 = 2

2 * 2 – 2 = 2

2 * 3 – 3 = 3

3 * 4 – 4 = 8

8 * 5 – 5 =35

35 * 6 – 6 = 204

## Number Series Part 4

Problem 1: 3   20   88   273   ?   559

3 * 5 + 5 = 20     (5=5*1)

20 * 4 + 8 = 88  (8=4*2)

88 * 3 + 9 = 273 (9=3*3)

273*2 + 2*4 = 554

554*1 + 1*5 = 559

Problem 2: ?   48  96   240   720   2520

48 * 2 = 96

96 * 2.5 = 240

240 * 3 = 720

720 * 3.5 = 2520

1.5=$\frac{3}{2}$

$\frac{48\times&space;2}{3}=32$

Problem 3: 1   ?   6   21   88   445

6 * 3 +3 = 21

21 * 4 + 4 = 88

88 * 5 + 5 = 445

1 * 1 + 1 = 2

2 * 2 + 2 = 6

Problem 4: 6   4   5   11   ?   361

6 * 0.5 + 1 = 4

4 * 1 + 1 = 5

5 * 2 + 1 = 11

11 * 4 + 1 =45

45 * 8 + 1 =361

Problem 5: 180   179  183   156   172   ?

180 – 179 = -1 = $1^{3}$

179 -183 = +4 = $2^{2}$

183 – 156 = -27 = $3^{3}$

156 – 172 = +16 = $4^{2}$

$-5^{3}=125$

172 – 125 = 47