Answer: Choice D) 8, 4, 2, 1, 1/2, 1/4
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Step-by-step explanation:
Each term of sequence D has us multiply by 1/2, or divide by 2, to get the next term.
8 * (1/2) = 4
4 * (1/2) = 2
2 * (1/2) = 1
1 * (1/2) = 1/2
(1/2) * (1/2) = 1/4
and so on
We can divide any term, except the first term, by its prior term to get the common ratio, so for instance,
common ratio = (term2)/(term1) = 4/8 = 1/2
and if we apply this to all possible pairs of consecutive terms then we see that we get 1/2 across the board. This confirms we have a geometric sequence.
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The other sequences do not fit this pattern.
For example, choice B has
(term2)/(term1) = 10/(-7) = -1.43
and
(term3)/(term2) = 23/10 = 2.30
those results are not the same; therefore, sequence B is not geometric. The other answer choices can be ruled out in a similar fasion.