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## Explanation Number Sequences Medium

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1. This sequence consists out of two alternating series.

-2   5   -4   3   -6   1

1. The first series shows the relation between the 1st and 3rd number, 3rd and 5th etc. in this case this following relation exists: 2 – 2 = -4 -4 – 2 = -6
2. The second series shows the relation between the 2nd and 4th number, the 4th and 6th etc. in this case 5-2=3
3. This means that a subtraction of 2 is executed on every number. The next number in the sequence will thus be 3-2=1

2. This sequence constists out of squares of the numbers. With increasing sequence the numbers which need to be squared are increasing with 1.

1   4   9   16   25   36

(=12)   (=22)   (=32)   (=42)   (=52)   (=62)

3. This sequence consists out of two alternating series.

75   15   25   5   15   3

1. The first series shows the relation between the 1st and 3rd number, 3rd and 5th etc. in this case this following relation exists: 75/25=3 25/15=5/3
2. The second series shows the relation between the 2nd and 4th number, the 4th and 6th etc. in this case 15/5=3
3. The next step is thus 5/(5/3)=3

4. This is an example of a factorial sequence.

1   2   6   24   120   720

1=1(=1!)
2=2*1(2!)
6=3*2*1(=3!)
24=4*3*2*1(=4!)
120=5*4*3*2*1 (=5!)

The next number in the sequence will be: 6*5*4*3*2*1(=6!)=720

5. This is a trick question and requires some out of the box thinking. Add +2 to every separate integer. For instance the the second number 305 = 1(+2)8(+2)3(+2) and this means that the last number will be 9(+2)6(+2)1(=2)=183

183   305   527   749   961   183

6. The difference increases with a factor of 2 with increasing sequence.

16   22   34   58   106   202

+6 +12 +24 +48 +96

7. The difference decreases with 2 with increasing sequence.

17   40   61   80   97   112

+23 +21 +19 +17 +15

8. This sequence consists out of two parts. The first row represents the difference between the sequence. Next the difference of the difference is taken and it is seen that the second difference always the first difference is in negative form.

55   34   21   13   8   5

-21 -13 -8 -5 -3

+8 +5 +3 +2

Take for example 55-21=34 and 34-13=21. The differences are -21 and -13 with a difference of +8 between -21 and -13. The 3rd difference of the sequence will thus be -8.

9. The difference decreases with a factor of 2 with increasing sequence.

259   131   67   35   19   11

-128  -64   -32   -16   -8

10. The difference decreases with 2 with increasing sequence

93   74   57   42   29  18

-19   -17   -15   -13   -11

11. This sequence consists out of two alternating series.

7   21   14   42   28   84

1. The first series shows the relation between the 1st and 3rd number, 3rd and 5th etc. in this case this following relation exists: 14-7=7 and 28-14=14.
2. The second series shows the relation between the 2nd and 4th number, the 4th and 6th etc. in this case 42-21=21
3. This means the series are increasing with a factor of 2 with increasing sequence. The next number in the sequence will thus be 42*2=84

12. The difference decreases with 6 with increasing sequence.

2   -12   -32   -58   -90   -128

-14   -20   -26   -32   -38

13. The following sequence is a addition of 3 to the power of 2.

0   9   36   81   144   225

32=9,    62=36,    92=81,    122=144,    152=225