It is possible to find a polynomial of order 7 that will fit the given numbers and any other number. Other functions are also possible.
The following polynomial, of order 6, fits them:
Un = (-5n6 + 114n5 - 1020n4 + 4540n3 - 10465n2 + 11696n - 4800)/60 for n = 1, 2, 3, etc.
With this rule, the next number is -160.
However, the answer that is most likely being sought is that the numbers in odd position are the counting numbers and the ones in even positions are their squares. With that rule, the next number would be 16.
Technically, any of these answers is correct. But you will only get marks for the last answer unless your teacher is a true mathematician.
The sequence provided is the Fibonacci sequence, where each number is the sum of the two preceding ones. In this case, after 1, 1, 2, 3, and 5, the next number is 3 + 5, which equals 8. Therefore, the next logical number in the sequence is 8.
1+1=2 : 1+2=3 : 2+3=5 : 3+5=8Therefore the next number is 8
The sequence 0, 3, 8, 15 can be understood by observing that each term can be expressed as (n^2 - 1), where (n) is the position in the sequence starting from 1. For example, (1^2 - 1 = 0), (2^2 - 1 = 3), (3^2 - 1 = 8), and (4^2 - 1 = 15). Following this pattern, the next term for (n = 5) would be (5^2 - 1 = 24). Thus, the next number in the sequence is 24.
456789
The given sequence consists of the cubes of consecutive integers: (1^3 = 1), (2^3 = 8), (3^3 = 27), and (4^3 = 64). The next integer is 5, so the next term in the sequence is (5^3 = 125). Thus, the next term is 125.
The sequence provided is the Fibonacci sequence, where each number is the sum of the two preceding ones. In this case, after 1, 1, 2, 3, and 5, the next number is 3 + 5, which equals 8. Therefore, the next logical number in the sequence is 8.
1+1=2 : 1+2=3 : 2+3=5 : 3+5=8Therefore the next number is 8
The next number is 4, followed by -2
8 -1 then +3
The next number in the sequence is 18. It's +1, +2, +3, +4, ....
456789
4
You add two then take one. 1+2=3, 3-1=2, 2+2=4, 4-1=3. The next number is 5.
The given sequence consists of the cubes of consecutive integers: (1^3 = 1), (2^3 = 8), (3^3 = 27), and (4^3 = 64). The next integer is 5, so the next term in the sequence is (5^3 = 125). Thus, the next term is 125.
Zero
Sequence is +4 - 3 + 5 - 2 + 6 - 1 (+1 - 1)2 6 3 8 6 12 next number 11
13, 21 - it is the Fibonacci sequence