Let's start by first remembering what a "geometric sequence" is. A geometric sequence is a sequence of numbers that multiply by the same number each time. For example, 2, 4, 8, 16 is a geometric sequence since each number is multiplied by 2 from one to the next, but 2, 4, 6, 8 is NOT a geometric sequence. We are adding 2 each time, but not multiplying, so it doesn't count. We have to be multiplying to have a geometric sequence.
[A] Let's look at A, are we multiplying by the same thing? 6*3 = 18 18*3 = 54 54*3 = 162 162*3 = 486 Yes! We are multiplying by 3 each time. This is a geometric sequence!
[B] Are we multiplying by the same thing? 2*3/2 = 3 3*3/2 = 9/2 which is not 5. NOPE
[C] Are we multiplying by the same thing? 2*5/2 = 5 5*5/2 = 25/2 which is not 8 NOPE
[D] Are we multiplying by the same thing? -4*1/2 = -2 -2*1/2 = -1 -1*1/2 = -0.5 -0.5*1/2 = -0.25 -0.25*1/2 = -0.125 Yep, we are multiplying by 1/2 each time! This is a geometric sequence!
