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Common Ratio Formula:
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The common ratio (r) is the constant factor between consecutive terms in a geometric sequence. 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 common ratio formula:
Where:
Explanation: The common ratio is calculated by dividing any term in the sequence by the previous term. This ratio remains constant throughout a geometric sequence.
Details: Calculating the common ratio is essential for identifying geometric sequences, predicting future terms, and understanding the growth or decay pattern of sequential data in mathematics, finance, and science.
Tips: Enter the current term and the next term from your 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 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 does a common ratio greater than 1 indicate?
A: A common ratio greater than 1 indicates exponential growth in the sequence, while a ratio between 0 and 1 indicates exponential decay.
Q4: What if the common ratio is zero?
A: If the common ratio is zero, all subsequent terms after the first non-zero term will be zero, creating a truncated sequence.
Q5: How is the common ratio used in real-world applications?
A: The common ratio is used in compound interest calculations, population growth models, radioactive decay, and many other exponential growth/decay scenarios.