Geometric sequence calculator

Number of input items(n):
First Item(a1):
Common ratio(q):
Geometric sequence：

A Geometric Sequence Calculator is a tool that helps calculate the terms of a geometric sequence, including the nth term and the sum of the sequence.

What is a Geometric Sequence?

A geometric sequence (or geometric progression) 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 (denoted as "r"). The general form of a geometric sequence is:

a,ar,ar2,ar3,…

Where:

  • a is the first term
  • r is the common ratio
  • The nth term is given by a×rn−1

Why Use a Geometric Sequence Calculator?

A calculator for geometric sequences simplifies the process of:

  • Finding the nth term of a sequence without manually calculating each term.
  • Quickly determining the sum of the sequence (for both finite and infinite sequences).
  • Solving real-world problems involving growth patterns, such as population growth, financial interest, or physics problems involving exponential growth/decay.

When to Use It?

You would use a geometric sequence calculator when you encounter problems where quantities increase or decrease in a consistent multiplicative way, such as:

  • Finance: Calculating compound interest or future value of investments.
  • Physics: Modeling exponential growth or decay.
  • Population Studies: Modeling population growth under ideal conditions.
  • Computer Science: Solving recursive problems or algorithms with geometric progression.