Home
Back
Geometric Sequence Formula:
| From: | To: |
The geometric sequence formula calculates the nth term of a geometric progression, where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
The calculator uses the geometric sequence formula:
Where:
Explanation: The formula calculates any term in a geometric sequence by starting with the first term and multiplying by the common ratio raised to the power of (n-1).
Details: Geometric sequences are fundamental in mathematics, finance, physics, and computer science. They model exponential growth and decay patterns found in population growth, radioactive decay, compound interest, and many other real-world phenomena.
Tips: Enter the first term (a1), common ratio (r), and the term number (n) you want to calculate. All values must be valid numbers with n being a positive integer.
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 |r| < 1, the terms get smaller and approach zero as n increases, representing exponential decay.
Q4: What if the common ratio is greater than 1?
A: If |r| > 1, the terms get larger as n increases, representing exponential growth.
Q5: Can the first term be zero?
A: If the first term is zero and the common ratio is non-zero, all terms will be zero. If both first term and common ratio are zero, the sequence is undefined.