Geometric Sequence Calculator

Enter value and click on calculate. Result will be displayed.

Formula:
an = a1 rn-1

Select calculator :

Enter the first term (a1) :
Enter the common ratio (r) :
Enter total number of terms (n) :
Result:

What is a Geometric Sequence Calculator?

A Geometric Sequence Calculator is a tool used to find terms, sums, and properties of a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio (r).

Why Use a Geometric Sequence Calculator?

  • Helps in mathematics, finance, and engineering for pattern analysis.
  • Used in compound interest, population growth, and physics problems.
  • Speeds up calculations of large sequences.

How to Calculate a Geometric Sequence?

  1. Nth Term Formula
an=a1×r(n−1)

Where:

  • aₙ = nth term
  • a₁ = first term
  • r = common ratio
  • n = term number
  1. Sum of First n Terms (Finite Sequence)
  1. Sum of Infinite Sequence (If |r| < 1)

Example:
If a₁ = 3, r = 2, and n = 5,

When to Use a Geometric Sequence Calculator?

  • Calculating compound interest in finance.
  • Analyzing population growth or radioactive decay.
  • Designing computer algorithms or fractal patterns.
  • Studying physics waves, oscillations, and investment returns.