Number Sequences Puzzle

The Puzzle:

Number Sequences
There are infinitely many formulas that will fit any finite series.

Try to guess the next number in each sequence using the simplest mathematical operations or ideas (you may get a different answer than my solution though):

· 8723, 3872, 2387, ?
· 1, 4, 9, 18, 35, ?
· 23, 45, 89, 177, ?
· 7, 5, 8, 4, 9, 3, ?
· 3, 8, 15, 24, 35, ?
· 2, 4, 5, 10, 12, 24, 27, ?
· 1, 3, 4, 7, 11, 18, ?
· 99, 92, 86, 81, 77, ?
· 0, 4, 2, 6, 4, 8, ?
· 1, 2, 6, 24, 120, ?
· 5, 7, 12, 19, 31, 50, ?
· 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, ?
· 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, ?
· 4, 7, 15, 29, 59, 117, ?
· 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, ?
Do you have the answer? Check against our solution!