### Home > CALC > Chapter 10 > Lesson 10.4.1 > Problem10-137

10-137.

For each of the geometric series state the common ratio “r” and determine the sum of the series.

1. 2.5 + 0.75 + 0.225 + 0.0675 + …

2. $\displaystyle\sum _ { k = 1 } ^ { \infty } 4 ( \frac { - 3 } { 5 } ) ^ { k }$

3. $\frac { 2 } { 15 } + \frac { 1 } { 5 } + \frac { 3 } { 10 } + \frac { 9 } { 20 } + \ldots$

4. $- 3 + \frac { 12 } { 5 } - \frac { 48 } { 25 } + \frac { 192 } { 125 } -$

$S=\frac{a}{1-r}$

$r=\frac{0.75}{2.5}$

$S=\frac{2.5}{1-0.75/2.5}$

$r=\frac{-3}{5}$

$a=4\Big(\frac{-3}{5}\Big)^1$

$r=\frac{3}{2}$

What does this tell you about the sum of the series?

$r=\frac{12/5}{-3}$