Geometric Sequence Calculator

Calculate the nth term and sum of a geometric sequence from the first term, common ratio, and number of terms.

Find the nth term and geometric series sum from one focused input set

Use this geometric sequence calculator when you want the nth term of a geometric progression, the sum of the first `n` terms, and a quick preview of the sequence without working through repeated multiplication by hand.

First term Common ratio Number of terms

Enter the first term, common ratio, and number of terms to calculate the sequence.

No result

Enter the sequence inputs to calculate the nth term.

The nth term, geometric series sum, and first terms preview will appear here.

This tool uses the geometric-sequence formulas for the nth term and the sum of the first `n` terms.

Enter the first term of the geometric sequence.
Enter the common ratio between consecutive terms.
Enter how many terms the sequence contains.
Review the nth term result, the sum of the first `n` terms, and the first-terms preview.
Use the formula cards to confirm how the geometric-sequence result was calculated.

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This tool calculates the nth term of a geometric sequence and the sum of the first `n` terms from one compact input set. It also shows the common ratio, a preview of the first few terms, and the formulas used in the result.

A geometric sequence is the ordered list of terms where each term is multiplied by a constant ratio. A geometric series is the sum of those terms. This calculator shows both so you can check the pattern and the total in one place.

A geometric sequence calculator is useful for algebra review, repeated-growth patterns, decay models, worksheet practice, and geometric progression problems where you need the nth term, the series sum, or both.

What is a geometric sequence?

A geometric sequence is a number pattern where each term is found by multiplying the previous term by the same constant value. That constant multiplier is called the common ratio.

What is the difference between a geometric sequence and a geometric series?

The sequence is the ordered list of multiplied terms. The series is the sum of those terms. This calculator returns both the nth term and the sum of the first `n` terms.

Can the common ratio be negative or fractional?

Yes. A negative common ratio alternates signs, and a fractional common ratio creates shrinking terms. This calculator supports both.

Does the number of terms need to be a whole number?

Yes. The number of terms must be a positive whole number because geometric sequences count discrete terms, not fractional positions.

Geometric Sequence Calculator

Calculate a geometric sequence instantly

Find the nth term and geometric series sum from one focused input set

Geometric sequence result

How to use the geometric sequence calculator