Tell whether the sequence 1/3,0,1,-2... I'd arithmetic, geometric,or neither. Find the next three terms of the sequence

Answer 1

1/3 to 0 is - 1/3
0 to 1 is one
so it is not an arithmetic sequence which is constant difference

1/3 * 0 = 0
0 * nothing I know of = 1
so it is not a geometric sequence

now let's see if we can find some other pattern
1/3 to 0 = - 1/3
0 to 1 = +1
1 to - 2 = -3
maybe
difference = -3 times previous difference?
-2 -3(-3) = -2+9 = 7
7 -3(9) = 7 - 27 = -20
-20 -3(-27) = 61
SO
1/3, 0 , 1 , -2 , 7, -20 , 61