Geometric Sequence Calculator

Simple and Accurate Tool

This geometric sequence calculator finds terms and the total sum. A geometric sequence multiplies each term by a fixed ratio. Enter your values and press Calculate. You will see clear results right away. The calculator shows the actual formulas used. Formulas appear for the nth term and the sum. Numbers show with trimmed decimals for a clean look. Very small or very large values may use scientific notation.

How It Works

The calculator follows standard geometric rules. Each term equals the first term times the ratio raised to a power. You enter three inputs, then the script computes the list and the sum. Results render in your browser almost instantly. The nth term formula is a_n = a1 × r^(n-1). For ratio equal to 1, the sum is a1 times n. For other ratios, use this sum formula. S_n equals a1 times 1 minus r^n. Then divide by 1 minus r.

Step-by-Step Instructions

Step 1: Input Your Values

Enter the first term a1. Use any positive or negative number. The calculator blocks zero for the first term. Decimals work well. Enter the common ratio r. Any number works, including decimals and negatives. Negative ratios flip the sign every step. Set r to 1 for a constant sequence. Enter the number of terms n. Use a whole number from 1 to 100. Long lists show a preview using the first and last five terms.

Step 2: Click "Calculate"

Click Calculate. Your results appear below the button. You will see the nth term formula used. You will see the sequence terms in order. You will see the sum and the exact sum formula. Extra notes include the last term. They may include a sum to infinity if the absolute value of r is less than 1 and r differs from zero. Notes also flag sign changes for a negative ratio. Press Calculate again after any change.

Benefits of This Tool

This geometric sequence calculator keeps math clear and fast. It runs fully in your browser. It uses trusted formulas and shows them on screen. A unique touch is the clear formula display. Numbers look clean for tiny or huge values. Use it to check homework steps and results. Model compound growth in finance with a fixed rate. Plan savings growth at a steady return. Study decay with a ratio between zero and one. Test sequences with a negative ratio to see sign flips. Keep your notes tidy with concise outputs.

Frequently Asked Questions

What counts as a geometric sequence? It multiplies each term by a constant ratio r. Can I enter decimals? Decimal inputs work for all fields. Can I use a negative ratio? The sequence alternates in sign with a negative ratio. What happens with r equal to 1? The sum equals a1 times n and terms repeat. Does it show a sum to infinity? It shows one when the absolute value of r is less than 1 and r differs from zero. Any input limits? Enter from 1 to 100 terms. The calculator requires a first term other than zero. How does it handle big or tiny values? It switches to scientific notation when values get extreme. Does it start with sample values? The page loads with sample values so you can see a result.

Final Thoughts

Use this geometric sequence calculator for quick, accurate work. It gives clear formulas, clean numbers, and helpful notes. Study, teach, or plan with confidence. We treat accuracy with the utmost care. Try it now and simplify your next sequence.