Question

Which of the following represents the geometric sequence?

I 1/4, 1/4, 1/4, 1/4

II 1/4, 1/5, 1/6, 1/7

III 1/4, 1, -4, 16

IV 1/4, -4, 1/4, -4

Answer 1

Answer is D. Hope it helps

Answer 2

The answer is sequence I (choice A)
The common ratio is r = 1 because we multiply each term by 1 to get the next term. No change happens when we multiply any number by 1. Another way to find the common ratio is to pick any term and divide it by its previous term.

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Choice B is not the answer because (1/5) divided by (1/4) = 0.2/0.25 = 0.8
and because (1/6) divided by (1/5) = 0.833 approximately. We don't get the same value each time. So the common ratio doesn't stay the same.

Choice C is not the answer either since most of the terms are positive but the -4 in slot 3 is not positive. If it was positive, then the common ratio would be 4 and this sequence would be geometric. If the terms alternated between positive and negative, then it would work as well (r would be r = -4)

Choice D has alternating terms of positive and negative, but there's no change in absolute value. There is no growth or decay as this the terms effectively stay the same. So there is no common ratio. This is why we can rule out choice D.