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
1+1 = 2 1+2 = 3 2+3 = 5 3+5 = 8 5+8 = 13
7, 6.
5
You add the last two numbers together to get the next number, and 3+5=8, so the answer is 8!
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
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
The sequence appears to be increasing at a variable rate. The pattern seems to be adding 1, then 3, then 5, then 10. Following this pattern, the next number in the sequence would be 20 + 15, which equals 35.
21. Add the last 2 numbers to get the next.
27
15
26
27
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.)