The next number is 12.
The rule is
Un = (2n4 - 27n3 + 123n2 - 214n + 120)/2 for n = 1, 2, 3, ...
13, 21 - it is the Fibonacci sequence
10, 8, 6, 4, 2, 0, -2, -4
The solution is 8. Here's the explanation: Differences between numbers that form sequence 200, 188, 152, 80, 8, ? form another sequence 12,36,72,72,? the solution of which is 0 because they are multiplied with 3, 2, 1, 0 respectively (72x0=0). When you apply 0 to the original sequence you get 8-0=8.
The solution is 8. Here's the explanation: Differences between numbers that form sequence 200, 188, 152, 80, 8, ? form another sequence 12,36,72,72,? the solution of which is 0 because they are multiplied with 3, 2, 1, 0 respectively (72x0=0). When you apply 0 to the original sequence you get 8-0=8.
The sequence indicates that one number is added to the previous number to find the value of the next number. Example 1 (+0) - 1 (+1) - 2 (+1) - 3 (+2) - 5 (+3) - 8 (+5) - 13. The next number in the sequence would be 21 (13 + 8).
What is the next number in this sequence 0,2,4,6,8......? Ans: The first number is 0. The second number is 2. The difference between those numbers is 2-0 = 2. The difference between the second and the third , the third and the fourth, the fourth and the fifty, the fifth and sixth is 2 only. So, the common difference is 2. That is 0+2=2, 2+2=4,4+2=6,6+2=8, then the next number in the series is 8+2 =10. The series continue like that only until infinity.
16
4
64
There are infinitely many different polynomials of degree 8 that will fit all the numbers of the above sequence. Each will generate a different number as the next one in the sequence.
The next number in the sequence is 48.