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Geometric Sequence Common Ratio Formula:
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The common ratio (r) in a geometric sequence is the constant factor between consecutive terms. It determines how each term relates to the previous one and defines the pattern of growth or decay in the sequence.
The calculator uses the geometric sequence common ratio formula:
Where:
Explanation: The common ratio is calculated by dividing any term in the sequence by the preceding term. This ratio remains constant throughout the entire geometric sequence.
Details: Calculating the common ratio is essential for understanding geometric sequences, predicting future terms, analyzing exponential growth or decay patterns, and solving problems in mathematics, finance, and science.
Tips: Enter the current term and the next term from your geometric sequence. Both values must be valid numbers, and the current term cannot be zero (division by zero is undefined).
Q1: What is a geometric sequence?
A: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Q2: Can the common ratio be negative?
A: Yes, the common ratio can be negative, which results in alternating positive and negative terms in the sequence.
Q3: What if the common ratio is between 0 and 1?
A: If 0 < r < 1, the sequence shows exponential decay. If r > 1, the sequence shows exponential growth.
Q4: How is the common ratio used in real-world applications?
A: Common ratios are used in compound interest calculations, population growth models, radioactive decay, and many other exponential growth/decay scenarios.
Q5: What's the difference between arithmetic and geometric sequences?
A: Arithmetic sequences have a constant difference between terms, while geometric sequences have a constant ratio between terms.