In a geometric sequence, you find the "common ratio" (not common difference) by dividing any term by the term that precedes it. This common ratio is the number you multiply each term by to get the next term in the sequence.
Here's a breakdown:
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Understanding Geometric Sequences: A geometric sequence is a list of numbers where each term is found by multiplying the previous term by a constant value (the common ratio).
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The Common Ratio (r): This is the key value that defines the geometric sequence.
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Finding the Common Ratio:
- Choose any two consecutive terms in the sequence.
- Divide the second term by the first term. The result is the common ratio (r).
Formula: r = an / an-1, where an is any term and an-1 is the term before it.
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Example:
Consider the geometric sequence: 2, 6, 18, 54, ...
To find the common ratio:
- Divide 6 by 2: 6 / 2 = 3
- Divide 18 by 6: 18 / 6 = 3
- Divide 54 by 18: 54 / 18 = 3
Therefore, the common ratio (r) is 3.
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Important Note: Make sure to perform the division between consecutive terms to correctly identify the common ratio. Do not subtract terms, as this would be relevant to arithmetic sequences, not geometric ones.
