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Question Determine the Sequence Is Arithmetic or Geometric Determine the Common Difference / Ratio Simplest Form.

Question

Question Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 72,12,2,ldots Answer Attempt 2out of 2 This is square sequence and the square is equal to square

Solution

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Answer

### This is a geometric sequence and the common ratio is equal to .

Explanation

## Step 1: Check for Arithmetic Sequence### To determine if the sequence is arithmetic, we check if there's a common difference between consecutive terms. The difference between the second term (12) and the first term (72) is . The difference between the third term (2) and the second term (12) is . Since the differences are not equal, the sequence is not arithmetic.## Step 2: Check for Geometric Sequence### To determine if the sequence is geometric, we check if there's a common ratio between consecutive terms. The ratio of the second term (12) to the first term (72) is . The ratio of the third term (2) to the second term (12) is . Since the ratios are equal, the sequence is geometric.