Geometric Sequence Calculator
Calculate geometric sequence terms, ratios, and sums including infinite series
About this calculator
A geometric sequence calculator helps you find terms, common ratios, and sums in geometric progressions where each term is found by multiplying the previous term by a constant ratio. This powerful tool is essential for students, mathematicians, and professionals working with exponential growth or decay problems, financial calculations involving compound interest, and advanced mathematical sequences. It can calculate individual terms, determine missing values, find partial sums, and even compute infinite series sums when the ratio is between -1 and 1.
How to use
Enter the first term and common ratio of your geometric sequence, then specify which term you want to find or how many terms to sum. The calculator will instantly compute the requested values, showing step-by-step solutions. For infinite series, ensure the common ratio is between -1 and 1 for convergence.
Frequently asked questions
What is a geometric sequence?
A geometric sequence is a series of numbers where each term is found by multiplying the previous term by a fixed constant called the common ratio.
How do I find the common ratio?
Divide any term by the previous term in the sequence. This quotient should be the same throughout the entire geometric sequence.
When does an infinite geometric series converge?
An infinite geometric series converges only when the absolute value of the common ratio is less than 1 (|r| < 1).