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R Sequence Formula:
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R sequence refers to a mathematical sequence where each term is obtained by multiplying the previous term by a constant value called the common ratio. This is the fundamental property of geometric sequences.
The calculator uses the R sequence formula:
Where:
Explanation: The formula calculates the next term in a geometric sequence by multiplying the previous term by the common ratio.
Details: R sequences (geometric sequences) are widely used in mathematics, finance (compound interest), computer science, physics, and many other fields where exponential growth or decay patterns occur.
Tips: Enter the previous term value and the common ratio. The calculator will compute the current term in the sequence.
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: How is this different from an arithmetic sequence?
A: In an arithmetic sequence, each term is obtained by adding a constant value to the previous term, while in a geometric sequence, each term is obtained by multiplying the previous term by a constant value.
Q3: Can the common ratio be negative?
A: Yes, the common ratio can be any real number, including negative values, which would cause the sequence to alternate between positive and negative values.
Q4: What happens if the common ratio is between 0 and 1?
A: If the common ratio is between 0 and 1, the sequence will decrease exponentially, approaching zero as the number of terms increases.
Q5: What are some real-world examples of geometric sequences?
A: Examples include population growth (under ideal conditions), radioactive decay, compound interest calculations, and fractal patterns in nature.