Sum of the first n terms of a GP

The sum of the first terms of a geometric progression also admits a closed-form formula, valid however only when the common ratio is different from $1$.

Property — Sum of the first $n$ terms of a GP

For $q\ne 1$: $S_n = a_1 + a_1 q + a_1 q^2 + \cdots + a_1 q^{n-1} = a_1\,\frac{q^n - 1}{q - 1}.$ For $q = 1$ all the terms coincide and $S_n = n\,a_1$.

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Topics: Sequences
Concepts: Geometric progression
Methods: Sum of a geometric progression
Skills: Use formulas