# Finite geometric series word problems

Understanding and solving problems with the formula for a finite geometric series.
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### Problem

Antônio releases a pendulum. On the first swing, it passes through an arc of 32, space, c, m. With each swing, it passes through an arc start fraction, 9, divided by, 10, end fraction the length of the previous swing.
When it completes its 25, start superscript, t, h, end superscript swing, what is the total distance that the pendulum has traveled?