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Geometric Sequence Calculator.

Calculate a term and partial sum of a geometric sequence.

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Results update as you type.

Result: term: 48.000000 · sum: 93.000000 · firstTerm: 3.000000 · ratio: 2.000000 · index: 5.000000

Result

term: 48.000000 · sum: 93.000000 · firstTerm: 3.000000 · ratio: 2.000000 · index: 5.000000

Use Cases

Find any term in a geometric progression

Quickly determine the value of a specific term in a geometric sequence without manually multiplying repeatedly. Useful for homework, financial projections, or pattern analysis.

Example: For first term 5, common ratio 2, and term index 10, the 10th term is 2560.

Calculate the sum of the first n terms

Compute the cumulative total of a geometric series up to a certain term. Helpful for understanding growth patterns, savings with compound interest, or summing series in math problems.

Example: For first term 3, common ratio 0.5, and term index 5, the partial sum is 5.8125.

Frequently Asked Questions

What is a geometric sequence?
A geometric sequence 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. For example, 2, 6, 18, 54 is geometric with a common ratio of 3.
How is the nth term of a geometric sequence calculated?
The nth term is calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term index. This calculator uses that formula to find the term you specify.
What is a partial sum of a geometric sequence?
A partial sum is the sum of the first n terms of the sequence. For a geometric sequence, the sum S_n = a_1 * (1 - r^n) / (1 - r) when r ≠ 1. This calculator computes that sum for the given term index.

Tips & Common Mistakes

Tips

  • Ensure the common ratio is not zero, as a zero ratio would make all terms after the first zero, which is a degenerate case.
  • If the common ratio is negative, the terms will alternate in sign. The calculator handles this correctly, but be aware of the pattern.
  • For large term indices, the term value may become extremely large or small; the calculator provides the result in standard notation.
  • Double-check that the term index is a positive integer. The calculator expects a whole number for the term position.

Common Mistakes to Avoid

  • Entering the term index as the number of terms to sum, rather than the specific term position. The term index is used for both the term and the partial sum.
  • Using a common ratio of 1, which makes the sequence constant. The partial sum formula is different for r=1, but this calculator may not handle that case correctly.
  • Confusing the first term with the term at index 0. The first term corresponds to index 1, not 0.

Last updated: August 13, 2026