Geometric Sequence Calculator

Overview

This geometric sequence calculator computes each term and the sum of the sequence. It uses a constant multiplier to generate the next term. The tool displays results with clear formatting.

How to Use This Tool

Step-by-Step Instructions

1. Enter the first term. This value cannot be zero.
2. Enter the common ratio. This number multiplies each term to produce the next one.
3. Enter the number of terms. Choose a number between 1 and 100.
4. Click the "Calculate Sequence" button.

The results will show the formula for the nth term, the list of terms, the sum of the sequence, and some extra details.

Input Field Details

• First Term (a₁): The starting value of the sequence.
• Common Ratio (r): The multiplier used for each new term.
• Number of Terms (n): How many terms you want. Accepts numbers from 1 to 100.

Output Explanation

The output section shows several pieces of information:

• The nth term formula used to calculate the sequence.
• A list of the sequence terms. If there are many terms, only the first five and the last five are shown.
• The sum of the sequence and the formula used to calculate it.
• Extra details such as the last term. It also explains if the sequence has no sum to infinity when the ratio is one or more in absolute value.

Numbers are formatted to remove extra zeros. This keeps the results clear.

Limitations and Special Notes

Please use valid numbers in all fields. An alert appears if an input is invalid. The tool will not work if the first term is zero or if the number of terms is out of the accepted range. Results display cleanly without extra or unnecessary zeros.

Common Use Cases

• Students working on math homework.
• Teachers preparing lesson materials.
• Anyone needing quick sequence calculations.

Frequently Asked Questions

If you enter a wrong number or leave a field blank, the tool will show an alert. All broken links have been removed. Follow the steps above to see correct results.

Final Thoughts

This geometric sequence calculator makes math simple. The clear steps guide you from input to result. The tool formats numbers neatly and runs in your browser. It is a helpful aid for quick and reliable calculations.