what is the next number in the following sequence
3,-6,12,4,20
2nd term - 1st term = (-6)-(3) = -9
3rd term - 2nd term = (12)-(-6) = 12+6 = 18
4th term - 3rd term = (4)-(12) = -8
5th term - 4th term = (20)-(4) = 16
It looks like the odd-numbered differences
are going
-9, -8, -7, -6, -5, ...
And it looks like the even numbered
differences are going
18, 16, 14, 12, 10...
If so then let the 6th term be x
2nd term - 1st term = (-6)-(3) = -9
3rd term - 2nd term = (12)-(-6) = 12+6 = 18
4th term - 3rd term = (4)-(12) = -8
5th term - 4th term = (20)-(4) = 16
6th term - 5th term = (x)-(16) = -7
(x)-(16) = -7
x-16 = -7
x = 16-7
x = 9
So the 6th term is 9
Just for fun, let's get one more term.
Let the 7th term be y.
2nd term - 1st term = (-6)-(3) = -9
3rd term - 2nd term = (12)-(-6) = 12+6 = 18
4th term - 3rd term = (4)-(12) = -8
5th term - 4th term = (20)-(4) = 16
6th term - 5th term = (9)-(16) = -7
7th term - 6th term = (y)-(-7) = 14
(y)-(-7) = 14
y-7 = 14
y = 21
So the sequence goes:
3,-6,12,4,20,9,21
Edwin