Which of the following is a geometric sequence? 3, 6, 12, 24, … 4, 8, 12, 16, … 2, 4, 16, 256, …

Mathematics

1 answer:

Svetlanka [38]3 years ago

7 0

Answer:

The geometric sequence would be 3, 6, 12, 24 . . .

Step-by-step explanation:

A geometric sequence is when the you find the next term in the sequence by multiplying by a common ratio. (A common ratio is the constant value that you multiply by each time in a geometric sequence.) In order to solve your problem, you would find the relationship between each term in the sequence. For the first sequence, 3, 6, 12, 24, etc., you can see that the ratio between one term and the next would be two: 3×2 = 6, 6×2 = 12, 12×2 = 24, and so on. This makes it a geometric sequence, but you still need to check the other sequences to make sure. For the sequence 4, 8, 12, 16, . . . , you need to add four each time. This means that the sequence has a common difference, or the constant value you add or subtract by in an arithmetic sequence. So, we know that the second sequence is not the answer. Finally, we check the last sequence, and if you look at it you can see that the you square the previous term to get the current one. This is different from a geometric sequence, and has a different name. However, it is not a geometric sequence because you are not multiplying by the same value each time (it doesn't have a common ratio). So, the first sequence, 3, 6, 12, 24, . . . , is a geometric sequence.

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