Next is 18.
The polynomial rule is
Un = (-5n4 + 74n3 - 301n2 + 478n - 24)/24 for n = 1, 2, 3, ...
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1+1=2 : 1+2=3 : 2+3=5 : 3+5=8Therefore the next number is 8
50
21
7, 2, -1, -2, -1 the next number in the sequence is 2. A constant difference of -5 is applied at each step with multiples of 2 increasing by 1 at each step being added. 7 - 5 + 0x2 = 2 2 - 5 + 1x2 = -1 -1 -5 + 2x2 = -2 -2 -5 + 3x2 = -1 -1 -5 + 4x2 = 2 2 - 5 + 5x2 = 7
21. Add the last 2 numbers to get the next.