Home/Algebra/Sequences, finite series, and recurrences/Finite geometric sum14. Sequences, finite series, and recurrencesFinite geometric sumLevel: fundamentalIn 14. Sequences, finite series, and recurrencesFormulaCopy LaTeXSn=a11−rn1−r (r≠1)S_n=a_1\frac{1-r^n}{1-r}\;(r\ne1)Sn=a11−r1−rn(r=1)Tagsalgebraalgebra formulasequencessequences series finitasDetailSum of n terms of a geometric sequence.Found an error? Contact us.Related formulasRelatedGeometric sequencean=a1rn−1a_n=a_1r^{n-1}an=a1rn−1Open formulaOpen in sectionRelatedInfinite geometric series∑k=0∞ark=a1−r,∣r∣<1\sum_{k=0}^{\infty}ar^k=\frac a{1-r},\quad |r|<1k=0∑∞ark=1−ra,∣r∣<1Open formulaOpen in section