Verified answer

1, 4, 7, 28, 31, 124, 127, 508

(x4, +3)

1, -2, 2, -4 , 0, 0, 4, -8

(x -2, +4)

2, 3, 5 , 8, 13 , 21, 34, 55, 89

(Fibonacci series, adding two previous numbers)

1, 5, 30 , 210 , 1680, 15120, 151200, 1663200

(x5, x6, x7, x8...)

34, 102, 105, 108,...

That's the first one!

Do your own homework Sherlock.

1,4,7,28,31,124,127,508

1,-2,2,-4,0,0,4,-8

2,3,5,8,13,21,34,55,89,144

1,5,30,210,1680,13440,120960,1209600