Geometric Sequence & Series (GP) Calculator (nth Term & Infinite Sum)
Calculate the nth term (aₙ), finite series sum (Sₙ), and convergent infinite geometric series sum (S∞) using the common ratio r and initial term a₁.
Calculator Inputs
Live Real-TimeValue of the nth Term (aₙ)
Sum of First n Terms (Sₙ)
6,560 sum
Infinite Convergent Sum (S∞)
0 sum
Exponential Acceleration: With r > 1, terms multiply at an exponential rate.
Geometric Progression Summary
Detailed Calculation Breakdown
Calculation Methodology
nth Term: aₙ = a₁ * r^(n-1). Finite Sum: Sₙ = a₁ * [(1 - r^n) / (1 - r)]. Infinite Convergent Sum (|r| < 1): S∞ = a₁ / (1 - r).
Important Legal & Educational Disclaimer
This exponential algebra tool computes geometric sequences and series expansions.
This calculator is designed for educational and informational purposes only based on public statutory frameworks. The outputs do not constitute binding financial, tax, or legal advice. We assume no liability for decisions made based on these estimations. Always verify with the relevant official authorities or a certified professional advisor.
Frequently Asked Questions
Related Calculators
Recommended tools and calculators tailored to your current calculation
Logarithm Calculator (Natural Log ln, Base 10, Base 2, Arbitrary Base)
Calculate natural logarithms (ln), common logarithms (log10), binary logs (log2), and arbitrary base logarithms log_b(x) using the change of base rule.
Arithmetic Sequence & Series (AP) Calculator (nth Term & Sum)
Calculate the nth term (aₙ), sum of the first n terms (Sₙ), common difference (d), and series mean for any arithmetic progression progression.
Percentage Increase, Decrease & Change Calculator ((New-Old)/Old × 100)
Calculate percentage increase, percentage decrease, absolute difference, growth rate, and ratio between two numerical values with step-by-step mathematical breakdown.
Matrix Determinant (2x2 & 3x3) & Invertibility Calculator
Calculate the exact determinant det(A) for 2x2 and 3x3 square matrices, check matrix invertibility, and solve systems of linear equations via Cramer's Rule.
Permutations (nPr) and Combinations (nCr) Math Calculator
Calculate permutations with order nPr, combinations without order nCr, and factorials n! for advanced probability and combinatorics calculations.
Classical Probability & Odds Ratio Math Calculator
Calculate theoretical event probability P(E), percentage likelihood, complementary probability P(E'), and odds ratio in favor vs against for statistical sample spaces.
Standard Deviation, Variance & Mean Statistics Calculator (σ & s)
Calculate population standard deviation (σ), sample standard deviation (s), variance (σ² & s²), arithmetic mean, and coefficient of variation (CV%) with full computational steps.
Scientific Notation & Standard Form Converter Calculator (a × 10ⁿ)
Perform multiplication, division, and conversions between standard decimal numbers and scientific exponential notation (a × 10ⁿ) with positive and negative powers of ten.