Questions: Algebra 1 Sem 2 Quiz 6.3.1 - Compare Arithmetic and Geometric Value: 2 Is the sequence arithmetic or geometric? 1,2,4,8,16, a. Arithmetic because there is a common difference of 2 b. Geometric because there is a common ratio of 2 . c. Arithmetic because there is a common ratio of 2 . d. Geometric because there is a common difference of 2 .

Algebra 1 Sem 2
Quiz 6.3.1 - Compare Arithmetic and Geometric

Value: 2
Is the sequence arithmetic or geometric?
1,2,4,8,16,
a. Arithmetic because there is a common difference of 2
b. Geometric because there is a common ratio of 2 .
c. Arithmetic because there is a common ratio of 2 .
d. Geometric because there is a common difference of 2 .
Transcript text: Algebra 1 Sem 2 Quiz 6.3.1 - Compare Arithmetic and Geometri Value: 2 Is the sequence arithmetic or geometric? $1,2,4,8,16$, a. Arithmetic because there is a common difference of 2 b. Geometric because there is a common ratio of 2 . c. Arithmetic because there is a common ratio of 2 . d. Geometric because there is a common difference of 2 .
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Solution

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Solution Steps

Step 1: Identify the type of sequence

The given sequence is \(1, 2, 4, 8, 16\). To determine whether it is arithmetic or geometric, we need to check for a common difference or a common ratio.

Step 2: Check for a common difference

An arithmetic sequence has a common difference between consecutive terms. Calculate the differences:

  • \(2 - 1 = 1\)
  • \(4 - 2 = 2\)
  • \(8 - 4 = 4\)
  • \(16 - 8 = 8\)

The differences are not the same, so the sequence is not arithmetic.

Step 3: Check for a common ratio

A geometric sequence has a common ratio between consecutive terms. Calculate the ratios:

  • \(\frac{2}{1} = 2\)
  • \(\frac{4}{2} = 2\)
  • \(\frac{8}{4} = 2\)
  • \(\frac{16}{8} = 2\)

The ratios are the same, so the sequence is geometric with a common ratio of 2.

Final Answer

The correct answer is B.

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