EVERYDAY CLARITY
Geometric Sequence Calculator
What is the nth term and finite sum of a geometric sequence? Enter the values below to calculate the result.
Your result
term
sum
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| First term | Enter first term using the definition in the method and example. |
| Common ratio | Enter common ratio using the definition in the method and example. |
| Term count (count) | Enter term count in count; use the same basis as the other measurements. |
Understanding your result
Read term, sum in the units and model stated on this page. The formula term=n==1 ? a1 : a1*r^(n-1) · sum=r==1 ? n*a1 : a1*(1-r^n)/(1-r) defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Mixing input units or changing the physical meaning of a variable without changing the model.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
What is the nth term and finite sum of a geometric sequence?
What is the nth term and finite sum of a geometric sequence? Enter the values below to calculate the result.
Common uses
- What is the nth term and finite sum of a geometric sequence
How it works
term=n==1 ? a1 : a1*r^(n-1); sum=r==1 ? n*a1 : a1*(1-r^n)/(1-r)
Worked example
Enter First term: 2 ; Common ratio: 3 ; Term count: 4 count. Results: term: 54 ; sum: 80 .