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Chapter 11: Q. 280 (page 1069)

In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio.

3,12,48,192,768,3072,...

Short Answer

Expert verified

The sequence is geometric and the common ratio is 4.

Step by step solution

01

Step 1. Given and explanation.

We have 3,12,48,192,768,3072,...
Geometric sequence is a ratio where the difference between the two continuous terms is always the same. This ratio is called common difference.
So to determine whether it is a geometric sequence or not, we need to calculate the ratio.

02

Step 2. Determining the ratio.

We have 3,12,48,192,768,3072,...
Ratio can be calculated as -

  1. 123=4
  2. 4812=4
  3. 19248=4
  4. 768192=4
  5. 3072768=4

As we can see that the ratio is the same in every term, we conclude that the sequence is geometric with common ratio as 4.

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