Next is 18.
The polynomial rule is
Un = (-5n4 + 74n3 - 301n2 + 478n - 24)/24 for n = 1, 2, 3, ...
The sequence appears to involve a pattern where each number is derived from a combination of multiplication and addition. Starting from 1, the pattern is: 1 × 1 + 1 = 2, 2 × 2 + 1 = 5, 5 × 2 + 0 = 10, and 10 × 5 = 50. Following this pattern, the next number should be 50 × 5 = 250. Therefore, the next number in the sequence is 250.
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
The sequence appears to involve a pattern where each number is derived from a combination of multiplication and addition. Starting from 1, the pattern is: 1 × 1 + 1 = 2, 2 × 2 + 1 = 5, 5 × 2 + 0 = 10, and 10 × 5 = 50. Following this pattern, the next number should be 50 × 5 = 250. Therefore, the next number in the sequence is 250.
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
21. Add the last 2 numbers to get the next.
15
26
27
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.)