The pattern is based on the following equation:

10−2=8

30−10=20

68−30=38

130−68=62

Now, let's look at the second-order differences:

20−8=12

38−20=18

62−38=24

The second-order differences are increasing by 6 each time:

12,18,24,30

So, the next first-order difference should be:

62+30=92

Now, adding this to the last term:

130+92=222

The pattern is alternating between adding and multiplying by 2:
3+2=5

5×2=10

10+5=15

15×2=30.
The next term is 30+15=45.

This sequence is the factorials of consecutive numbers:
1!=1, 2!=2, 3!=6, 4!=24, 5!=120.
The next term is 6!=6×5×4×3×2×1=720.

The difference between each pair of consecutive numbers increases by 2:
16−7=9

27−16=11

40−27=13

40−27=13

55−40=15

The next difference should be 17, so 55+17=72.

Each number is multiplied by 4:
2×4=8, 8×4=32, 32×4=128, 128×4=512.
The next term is 512×4=2048.

A = 1, D = 4, I = 9, P = 16

Observing the numbers:

1 → 4 → 9 → 16 → ?

The difference sequence is: +3, +5, +7, ...

The next difference should be +9 and the corresponding letter will be 16 (P) + 9 = 25 (Y).

The positions of the letters decrease in steps of 2, then 3:
Z (26th), X (24th), V (22nd), T (20th), R (18th).
The next letter should be R (18) - 2 = P (16).

The series alternates between starting with A and going backwards:
Z (26), Y (25), X (24), W (23), ?, which corresponds to the letter W (23) - 1 = V (22).

The positions increase by a constant difference of 3:
M (13th), P (16th), S (19th), V (22nd), Y (25th).
The difference between the terms is 3.
The next term will be Y (25) + 3 = 28

Since the alphabet has 26 letters, letter 28 loops back to B.

The positions of the letters are increasing by 4 each time:
G (7th), K (11th), O (15th), S (19th), W (23rd).
The next term will be W (23) + 4 = 27

Since the alphabet has 26 letters, letter 27 loops back to A.
So, the next letter is A.