Geometric Series (Sum) Calculator
Sum of the first n terms of a geometric progression.
Formula first
Overview
This formula calculates the sum of a finite sequence where each successive term is generated by multiplying the previous term by a constant factor known as the common ratio. It serves as a mathematical tool for aggregating exponential growth or decay over a specific number of intervals.
Symbols
Variables
= Sum, a = First Term, r = Common Ratio, n = Num Terms
Apply it well
When To Use
When to use: Use this formula when you need to find the total sum of a sequence where the ratio between any two consecutive terms is constant. It is applicable only when the common ratio is not equal to one and the series has a definite, finite number of terms.
Why it matters: This equation is fundamental in finance for calculating the future value of annuities and loan amortizations. It is also used in physics to model wave dampening and in computer science to determine the time complexity of divide-and-conquer algorithms.
Avoid these traps
Common Mistakes
- Using n-1 instead of n in power.
- Assuming infinite sum.
One free problem
Practice Problem
Calculate the sum of the first 5 terms of a geometric progression where the first term is 10 and the common ratio is 2.
Solve for:
Hint: Calculate 2 to the power of 5 first, then substitute all values into the numerator and denominator.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Geometric series
- Calculus by James Stewart
- Britannica: Geometric series
- Stewart Calculus: Early Transcendentals
- Standard curriculum — A-Level Pure Mathematics (Sequences)