## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

The common ratio of a geometric sequence is equal to the quotient of any term and the term before it: $\ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}$ The sum of a convergent infinite geometric series is given by the formula: $S_{\infty}=\dfrac{a_1}{1-r}$ and a geometric series converges if $|r| \lt 1$. where $r \ =common \ ratio \ =\dfrac{3}{2}$ Since $r=|\dfrac{3}{2}| \gt 1$, the infinite geometric series diverges.