The number series follows the following rule

                           2                12               23               35               48                 62

   Difference:             10               11               12                13                14

The number series actually consists of two separate series

Series-1:                  11           14           17          20         23

            Difference:                      3              3            3           3       

            Series-2:                  9             12           15          18

            Difference:                       3              3             3   

The number series follows the following rule

1st number  = 1
2nd number = 2
3rd number  = 1x2 = 2 (Multiplication of 1^st & 2^nd)
4th number  = 2x2 = 4 (Multiplication of 2^nd  & 3^rd)
5th number  = 2x4 = 8 (Multiplication of 3^rd & 4^th)

6^th number = 4x8 = 32 (Multiplication of 4^th & 5^th)

7^th number = 8x32 = 256 (Multiplication of 5^th  & 6^th)

The number series follows the following rule

1st number = 1²+ 1
2^nd number = 2²+ 2
3^rd number = 3²+ 3
4^th number = 4²+ 4
5^th number = 5²+ 5

6^th number = 6²+ 6

The number series follows the following rule

1st number = 0x1x2= 0
2^nd number = 1x2x3= 6
3^rd number = 2x3x4= 24
4^th number = 3x4x5= 60
5^th number = 4x5x6= 120

6^th number = 5x6x7= 210

The number series follows the following rule

1st number = 0x1+1 = 1
2^nd number = 1x2+2 = 4
3^rd number = 2x3+3 = 9
4^th number = 3x4+4 = 16
5^th number = 4x5+5 = 25

6^th number = 5x6+6 = 36

$$HereistheLaTeXrepresent\frac{9}{3},\frac{3}{3},\frac{1}{3},\frac{\frac{1}{3}}{3}$$

In the above number series, every preceding number is divided by 3 to get subsequent number.

                                                                       9/3, 3/3, 1/3, (1/3)/3

The number series actually consists of two separate series

Series-1:              13          14          15          16            17

            Difference:                  1            1             1            1

            Series-2:              11          12          13          14

            Difference:                  1             1             1

The number series follows the following rule

1st number = 753
2^nd number = 753+1 = 754
3^rd number =754+2 = 756
4^th number = 756+3 = 759
5^th number = 759+4 = 763

6^th number = 763+5 =768

The number series follows the following rule

1st number = 3
2^nd number = 3+1 = 4
3^rd number = 4+(1+2) =7
4^th number = 7+(1+2+3) = 13
5^th number = 13+(1+2+3+4) = 23

6^th number = 23+(1+2+3+4+5) = 38

7^th number = 38+(1+2+3+4+5+6) = 59