The next number is 67.
The simplest polynmial rule is
Un = (8n4 - 97n3 + 412n2 - 713n + 432)/6 for n = 1, 2, 3, ...
13, 21 - it is the Fibonacci sequence
5
7, 6.
1+1 = 2 1+2 = 3 2+3 = 5 3+5 = 8 5+8 = 13
25 is the next number that appears in that sequence.
1+1=2 : 1+2=3 : 2+3=5 : 3+5=8Therefore the next number is 8
50
-1.
13, 21 - it is the Fibonacci sequence
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
40.
21. Add the last 2 numbers to get the next.
27
15
26
27