It is easy to find a rule based on a polynomial of order 5 such that these numbers are the first five generated by the rule. There are also non-polynomial solutions.
A solution based on a polynomial of order 4 is
Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, ..., 5.
3, -6, 12, 4, 20, 13, 27, 21, 33 -9, +18, -8, +16, -7, +14, -6, +12
what is the pattern for the following 3, -6, 12, 4, 20
14
12/20=6/10=3/5 Do you see the pattern?
There is a "Fibonacci" like series is that each digit is the sum of the preceding two numbers: 4 + 8 = 12 8 + 12 = 20 So the series continues: 12 + 20 = 32 20 + 32 = 52 32 + 52 = 84 52 + 84 = 136 and so on. ----------------------------------------------------------------------------- What number do you want to be next? Give me a number and I'll give you a polynomial so that putting in 1, 2, 3, 4 gives the values 4, 8, 12, 20 and putting in 5 gives the number you want.
The given pattern appears to alternate between two sequences: one sequence that doubles the previous number (3 to 6 to 12) and another that adds 1 to the previous number (4 to 20). Following this pattern, after 20, the next number in the doubling sequence would be 24, as it continues from 12. Thus, the next number in the pattern is 24.
20/12 = 5/3 = 12/3
3, -6, 12, 4, 20, 13, 27, 21, 33 -9, +18, -8, +16, -7, +14, -6, +12
20/12 = 18/12 = 12/3
20 over 12 s a mixed number = 12/3
The sequence changes by multiplying with different numbers: from 3 to -6 (* -2), -6 to 12 (* -2), 12 to 4 (* 0.33), and 4 to 20 (* 5). If we continue this pattern, 20 multiplied by 0.5 gives us 10. So, the next number is 10.
what is the pattern for the following 3, -6, 12, 4, 20
14
3, -6, 12, 4, 20, ?
12/20=6/10=3/5 Do you see the pattern?
20/12 can not be expressed as a whole number but as a mixed number it is 1 and 2/3
There is a "Fibonacci" like series is that each digit is the sum of the preceding two numbers: 4 + 8 = 12 8 + 12 = 20 So the series continues: 12 + 20 = 32 20 + 32 = 52 32 + 52 = 84 52 + 84 = 136 and so on. ----------------------------------------------------------------------------- What number do you want to be next? Give me a number and I'll give you a polynomial so that putting in 1, 2, 3, 4 gives the values 4, 8, 12, 20 and putting in 5 gives the number you want.