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Sum of Geometric Sequence Calculator

Online geometric series calculator: sum the first n terms via a₁(1−q^n)/(1−q), or na₁ when q=1.

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S_n=a_1(1−q^n)/(1−q)
First
q=1 gives na1
Positive integer

📖 Tutorial | Geometric Sum

1. Definition
For q≠1, S_n=a₁(1−q^n)/(1−q); for q=1, S_n=na₁, derived by shifted subtraction.
2. Formula & Notation
S_nSum of n terms
3. Properties & Laws
  • Quotient formula for q≠1;
  • na₁ for q=1;
  • Exponential growth when q>1;
  • Linked to compound interest.
4. Steps
  1. Enter a₁, q, n;
  2. Click "Sum";
  3. Or click "Load Example".
5. Worked Examples
Example: 10 terms 1+2+… gives 1023.
6. Common Pitfalls
q=1 makes the denominator zero;
It is q^n;
Keep (1−q) consistent.

❓ FAQ | Geometric Sum

Formula?
a₁(1−q^n)/(1−q).
q=1?
na₁.
Growth?
Exponential.
Uses?
Compound interest.
Derive?
Shifted subtraction.
Negative q?
Still works.
q^n?
q to the nth power.