A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Examples of Geometric Sequences
Here are several examples to illustrate the concept:
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Example 1: 2, 4, 8, 16, ... This sequence has a common ratio of 2 (each term is multiplied by 2 to get the next). This is a classic and simple example often used in introductory explanations. (Source: Provided reference text)
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Example 2: 5, 10, 20, 40, 80, ... This sequence demonstrates a common ratio of 2. (Source: Tutorial 54D: Geometric Sequences and Series)
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Example 3: 2, 10, 50, 250, ... Here, the common ratio is 5. (Source: Mastering Formulas for Geometric Sequences (Review Video))
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Example 4: 1, 3, 9, 27, ... This sequence uses a common ratio of 3. (Source: Geometric Sequence Formulas)
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Example 5: 10, 5, 2.5, 1.25, ... This example shows that the common ratio can also be a fraction (0.5 in this case). (Source: Geometric progression - Wikipedia)
The common ratio is crucial in identifying and working with geometric sequences. It allows us to predict future terms and calculate sums of series. Understanding this concept is fundamental to further studies in mathematics.
