Given any number it is easy to find a rule based on a polynomial of order 7 such that the first seven numbers are as listed in the question and the eighth is the given number. That is, it is easy to find a rule so that any number can be the "next" in the sequence.
The polynomial of order six that fits is
Un = (n6 - 15n5 + 115n4 - 405n3 + 964n2 - 660n + 240)/240 and
accordingly, U8 = 379.
They are: 0, -5, -10
1, 2, 5, 10, 19, 38, 95, 190.
1 x 190, 2 x 95, 5 x 38, 10 x 19
30, 42, 38
280
They are: 0, -5, -10
the next three numbers are 180 540 and 1620=)
219
1, 2, 5, 10, 19, 38, 95, 190.
There is no number pattern in 781013. But there is a number pattern in the numbers 7, 8, 10, 13. 7+1=8 8+2=10 10+3=13 Can you see the pattern? And the next number in this sequence would be ... ?
The pattern seems to be +10 then -5. Therefore the next two numbers would be 26 and 36.
The pattern 1, 10, 100, 1000 next four numbers would be 10000, 100000, 1000000, 10000000.
The pattern is +5, -7... the answer is 6
These are all the whole numbers that go into 190 evenly: 1, 2, 5, 10, 19, 38, 95, 190.
-12, 14, -16
1 x 190, 2 x 95, 5 x 38, 10 x 19
The pattern is created by adding successive odd numbers. The next number is 50.