How to Use the Geometric Sequence Calculator
A geometric sequence has a constant ratio between consecutive terms. Enter the first term (a₁), common ratio (r), and term number (n) to instantly get the nth term and sum S_n.
Key Formulas
nth term: a_n = a₁ × r^(n−1)
Sum (r≠1): S_n = a₁ × (r^n − 1) / (r − 1)
Sum (r=1): S_n = n × a₁
Real-World Examples
Compound interest: $1,000 at 5% yearly → a_n = 1000 × 1.05^(n−1). Bacterial growth: 100 cells doubling every hour → after 8 hours = 100 × 2^7 = 12,800.
FAQ
What if r = 0?
A ratio of 0 makes all terms after the first equal to zero, which is not a meaningful geometric sequence. This calculator requires a non-zero first term.
Can large n cause overflow?
Yes. JavaScript's floating-point limit is about 1.8×10³⁰⁸. Very large ratios or term numbers can yield Infinity in the result.