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Recognizing Geometric Sequences

Recognizing Geometric Sequences 1.8 - Solution

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We are asked to compare the sequences shown below.

Sequence A
Sequence B

Since the way in which the terms change characterizes each type of sequence, we can analyze this to classify the sequences given. To do this, let's start by finding the difference between consecutive terms.

As we can see, Sequence A has a common difference of Therefore, it is an arithmetic sequence. On the other hand, we can see that Sequence B is not an arithmetic sequence, since the difference between its consecutive terms is not constant. We can now check for the ratios between consecutive terms.

Notice that Sequence B has a common ratio of Therefore, this is a geometric sequence. We can summarize our results as shown below.

  • The sequence is an arithmetic sequence with a common difference of
  • The sequence is a geometric sequence with a common ratio of