Number Series

From the given series, it is clear that every term is added to the increasing powers of 2 to get the next term.

0 + 2¹ = 2
2 + 2² = 6
6 + 2³ = 14
14 + 2⁴ = 30
Similarly, 30 + 2⁵ = 62

From the series, it is clear that every term of the series is multiplied by either 1/2 or 1/3 to get the next term.

60 * 1/2 = 30
30 * 1/3 = 10
10 * 1/2 = 5
5 * 1/3 = 5/3
Similarly, (5/3) * (1/2) = 5/6

From the series, it is clear that every term is the first prime number in its group, starting from 1 to 10.
2 is the first prime number between 1 to 10.
11 is the first prime number between 11 to 20.
23 is the first prime number between 21 to 30.
41 is the first prime number between 41 to 50.
Similarly, 53 is the first prime number between 51 to 60.

From the series, it is clear that every term of the series is subtracted by its half to get the next term.

100 - (100/2) = 50
50 - (50/2) = 25
25 - (25/2) = 12.5
Similarly, 12.5 - (12.5/2) = 6.25

From the series, it is clear that every term is the square of the consecutive terms.

11² = 121, 12² = 144, 13² = 169, 14² = 196. Similarly, 15² = 225.

From the series, it is clear that the terms are divided by consecutive numbers.

100/2 = 50, 50/3 = 50/3, (50/3)/4 = 25/6. Similarly, (25/6)/5 = 5/6.

From the series, it is clear that every term is multiplied by either 4 or 2 to get the next term.

1 * 4 = 4, 4 * 2 = 8, 8 * 4 = 32, 32 * 2 = 64, 64 * 4 = 256. Similarly, 256 * 2 = 512.

From the series, it is clear that every term is operated with the logic (3n - 2) to get the next term.

5 * 3 - 2 = 13, 13 * 3 - 2 = 37, 37 * 3 - 2 = 109

Similarly, 109 * 3 - 2 = 325.

From the series, it is clear that every term is added to 1 * 2, 2 * 3, 3 * 4..... as follows:

1 + 1 * 2 = 3, 3 + 2 * 3 = 9, 9 + 3 * 4 = 21, 21 + 4 * 5 = 41

Similarly, 41 + 5 * 6 = 71.

In the series, it is clear that every term is added to either 4 or 4² to get the next term.

6 + 4 = 10
10 + 4² = 26
26 + 4 = 30
30 + 4² = 46
46 + 4 = 50
Similarly, 50 + 4² = 66

From the series, it is clear that every term is added to a consecutive prime number to get the next term.

0 + 2 (prime number) = 2
2 + 3 (prime number) = 5
5 + 5 (prime number) = 10
10 + 7 (prime number) = 17
17 + 11 (prime number) = 28
Similarly, 28 + 13 = 41