Question

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

A.neither;7,-20,61 
B.geometric;7,-20,61 
C.arithmetic;1/3,1 1/3,3 
D.geometric;-3 1/3, 5 5/9,9 7/27

Answer 1

differences: -1/3, 1, -3
ratios: 0, ∞, -2

since neither is constant, it is neither an A.P. or a G.P.

So, how to figure the next terms?

Note that the differences form a G.P., with the next terms 9,-27,81

Adding those to -2, we get 7,-20,61, or choice (A)