Question

Identify which of the sequences below is a geometric sequence.

Answer 1

Answer:

The right answer is d. 3, 6, 12, 24, 48

Step-by-step explanation:

To find the right answer, we need to know that for a sequence to be a geometric sequence; each term has to be multiple of the previous term, and it has to be the same multiple for all terms.

we're going to check all the answer to seek the right answer.

Checking a. 1, 3, 5, 7, 9.

Three is three times 1, but 5 isn't multiple of 3, with this we can see a isn't the right answer.

Checking b. 2, 4, 6, 8, 10,

Four is twice 2, but 6 isn't multiple of 4, with this, we can see b isn't the right answer

Checking c. 2, 5, 7, 10, 12,

Five isn't multiple of 2 so, c isn't the right answer.

Checking d. 3, 6, 12, 24, 48,

Six is  twice three; twelve is twice six, twenty-four is twice twelve, and

forty-eight is twice twenty-four.

we can see that in d all the terms are multiples and twice the previous term, so this is the right answer.

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Answer 2

Answer: Choice D)  3, 6, 12, 24, 48

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Explanation:

Sequence A is not geometric. Dividing each term by its previous term does not lead to the same common ratio. For instance, 3/1 = 3 and 5/3 = 1.67

Sequence B is a similar story. We have 4/2 = 2 and -6/4 = -1.5

Sequence C is similar as well. This time 5/2 = 2.5 and 7/5 = 1.4

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Sequence D is geometric because dividing each term over its previous term leads to the same common ratio

6/3 = 2

12/6 = 2

24/12 = 2

48/12 = 2

The common ratio is r = 2.

Put another way, each term is multiplied by 2 to get the next term

3*2 = 6

6*2 = 12

12*2 = 24

24*2 = 48