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Uestion Etermine If the Sequence Below Is Arithmetic or Geometric and Determine the Common Tifference / Ratio in Simplest Form.

Question

uestion etermine if the sequence below is arithmetic or geometric and determine the common tifference / ratio in simplest form. 125,25,5,ldots Answer Attemperout of? 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### An arithmetic sequence has a constant difference between consecutive terms. The difference between 25 and 125 is . The difference between 5 and 25 is . Since the differences are not the same, this is not an arithmetic sequence.## Step 2: Check for Geometric Sequence### A geometric sequence has a constant ratio between consecutive terms. The ratio between 25 and 125 is . The ratio between 5 and 25 is . Since the ratios are the same, this is a geometric sequence.## Step 3: Determine the Common Ratio### The common ratio is the constant multiplier between consecutive terms, which we found to be .