Mathematical formulas

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Algebra
Sequences, finite series, and recurrences
Geometric sequence

14. Sequences, finite series, and recurrences

Geometric sequence

Level: fundamental

In 14. Sequences, finite series, and recurrences

Formula

a_n=a_1r^{n-1}

Tags

algebra
algebra formula
sequences
sequences series finitas

Detail

Each term is obtained by multiplying by a constant ratio.

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Finite geometric sum
$S_n=a_1\frac{1-r^n}{1-r}\;(r\ne1)$
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Infinite geometric series
$\sum_{k=0}^{\infty}ar^k=\frac a{1-r},\quad |r|<1$
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