The Geometric Sequence Calculator helps you find the terms of a geometric progression, the common ratio, and the nth term of the sequence. A geometric sequence is a series of numbers where each term is obtained by multiplying the previous term by a constant value known as the common ratio.

What is a Geometric Sequence?

A geometric sequence (or geometric progression) follows the pattern:
a, ar, ar², ar³, ...

Geometric Sequence Formula

a_n = a₁ × rⁿ⁻¹

Where:

• a_n = nth term of the sequence
• a₁ = first term
• r = common ratio
• n = term position

Examples

Example 1:

First term = 3
Common ratio = 2
Find the 5th term:
a₅ = 3 × 2⁴ = 3 × 16 = 48

Example 2:

First term = 5
Common ratio = 3
Find the 4th term:
a₄ = 5 × 3³ = 5 × 27 = 135

Example 3:

First term = 10
Common ratio = 0.5
Find the 6th term:
a₆ = 10 × (0.5)⁵ = 10 × 0.03125 = 0.3125

Example 4:

First term = -4
Common ratio = -2
Find the 3rd term:
a₃ = -4 × (-2)² = -4 × 4 = -16

This calculator is useful for algebra students, teachers, and anyone who works with patterns, exponential growth, and repeated multiplication.