Answer: Choice B) -3, 3, -3, 3, ....
=====================================
How I got that answer:
A sequence is geometric if you are able to divide any term over its prior one and get the same result each time. Note with something like choice A we have...
term2/term1 = 13/6 = 2.17 (approx) and term3/term2 = 19/13 = 1.46
the results 2.17 and 1.46 are not the same, so we can rule out choice A
---------
Choice B however, we have...
term2/term1 = 3/(-3) = -1
term3/term2 = -3/3 = -1
term4/term3 = 3/(-3) = -1
each time we get -1, so this is the common ratio. We can multiply each term by the common ratio -1 to get the next term, for instance,
term2 = (common ratio)*(term1) = -1*(-3) = 3
term3 = (common ratio)*(term2) = -1*3 = -3
and so on. This proves that sequence B is geometric. Sequences C and D are not geometric for similar reasoning to choice A.
