CPM Homework Help : APCALC Problem 10-155

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10-155.

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

$2.5 + 0.75 + 0.225 + 0.0675 + …$
Step 1 (a):
$r=\frac{0.75}{2.5}$
Step 2 (a):
$S=\frac{2.5}{1-0.75/2.5}$

$\displaystyle\sum _ { k = 1 } ^ { \infty } 4 ( \frac { - 3 } { 5 } ) ^ { k }$
Hint (b):
$r=\frac{-3}{5}$
More Help (b):
$a=4\Big(\frac{-3}{5}\Big)^1$

$\frac { 2 } { 15 } + \frac { 1 } { 5 } + \frac { 3 } { 10 } + \frac { 9 } { 20 } + \ldots$
Step (c):
$r=\frac{3}{2}$
What does this tell you about the sum of the series?

$- 3 + \frac { 12 } { 5 } - \frac { 48 } { 25 } + \frac { 192 } { 125 } -\ldots$
Step (d):
$r=\frac{12/5}{-3}$

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