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Chapter 12: Q 138. (page 1198)

In the following exercises, determine if each sequence is arithmetic, geometric or neither. If arithmetic, indicate the common difference. If geometric, indicate the common ratio.

4,8,12,24,48,96,...

Short Answer

Expert verified

The sequence is neither.

Step by step solution

01

Step 1.  Write the given sequence and use the definition of geometric sequence

The given sequence is:

4,8,12,24,48,96,...

A geometric sequence is a sequence where the ratio between consecutive terms is always the same.

The ratio between consecutive terms, anan-1, is r, the common ratio, where ris greater than or equal to two.

02

Step 2. Find the ratio of the consecutive terms.

84=2,128=32,2412=2,4824=2,9648=2

As we can see that the ratio of consecutive terms is not the same, therefore this sequence is not geometric.

03

Step 3. To determine if the sequence is arithmetic, find the difference of consecutive terms

8-4=4,12-8=4,24-12=12,48-24=24,96-48=48

As we can see that the difference of consecutive terms is not the same, therefore this sequence is not arithmetic.

This sequence is neither.

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