QuestionAugust 31, 2026

Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form. 32,8,2,ldots Answer Altemptiout of a This is square sequence and the square is equal to square

Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form. 32,8,2,ldots Answer Altemptiout of a This is square sequence and the square is equal to square
Determine if the sequence below is arithmetic or geometric and determine the common
difference/ratio in simplest form.
32,8,2,ldots 
Answer Altemptiout of a
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 \frac{1}{4}. Explanation 1. Identify the Type of Sequence Check if the sequence is arithmetic by finding the difference between consecutive terms: 8 - 32 = -24 and 2 - 8 = -6. Since the differences are not equal, it is not arithmetic. 2. Check for Geometric Sequence Divide consecutive terms to find the ratio: \frac{8}{32} = \frac{1}{4} and \frac{2}{8} = \frac{1}{4}. The ratios are equal, indicating a geometric sequence. 3. Determine the Common Ratio The common ratio is \frac{1}{4}.

Explanation

1. Identify the Type of Sequence<br /> Check if the sequence is arithmetic by finding the difference between consecutive terms: $8 - 32 = -24$ and $2 - 8 = -6$. Since the differences are not equal, it is not arithmetic.<br /><br />2. Check for Geometric Sequence<br /> Divide consecutive terms to find the ratio: $\frac{8}{32} = \frac{1}{4}$ and $\frac{2}{8} = \frac{1}{4}$. The ratios are equal, indicating a geometric sequence.<br /><br />3. Determine the Common Ratio<br /> The common ratio is $\frac{1}{4}$.
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