Next is 18.
The polynomial rule is
Un = (-5n4 + 74n3 - 301n2 + 478n - 24)/24 for n = 1, 2, 3, ...
1+1=2 : 1+2=3 : 2+3=5 : 3+5=8Therefore the next number is 8
50
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
21. Add the last 2 numbers to get the next.
1+1=2 : 1+2=3 : 2+3=5 : 3+5=8Therefore the next number is 8
50
13, 21 - it is the Fibonacci sequence
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
21. Add the last 2 numbers to get the next.
27
15
27
26
3,5,8,13 is followed by 21. 1,1,2,3,5,8,13,21,34,55,... is the Fibonacci series or Fibonacci sequence where the next number in the sequence is the sum of the last two numbers (1+1=2, 1+2=3, 2+3=5, etc.)
8, if it is the Fibonacci sequence; 7, if it the sequence of non-composite numbers (1 and primes); there are other possible answers.