Sequences

Geometric Series

Find finite geometric sums and connect them to growth, decay and finance contexts.

Sequences hubGeometric sequencesInfinite series

A geometric series is the sum of terms in a geometric sequence.

Finite geometric sum\[S_n=\frac{u_1(1-r^n)}{1-r}\qquad(r e1)\]

Worked example

Find the sum of \(4+12+36+\cdots\) for the first 6 terms.

Here \(u_1=4\), \(r=3\), and \(n=6\).

\[S_6=\frac{4(1-3^6)}{1-3}=1456\]

Common mistake

Do not confuse \(u_n\), which is a single term, with \(S_n\), which is the sum of terms.