CPM Homework Help : PC3 Problem 12-98

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12-98.

Write out the first four terms of each of the following sequences. Then evaluate $\lim\limits_ { n \rightarrow \infty } a _ { n }$ .

$a_n =\frac { 2 - n } { 3 + n }$
Steps (a):
$a_1=\frac{2-1}{3+1}=\:?$
$a_2=\frac{2-2}{3+2}=\:?$
$a_3=\frac{2-3}{3+3}=\: ?$
$a_4=\frac{2-4}{3+4}=\:?$

$a_n = \frac { ( - 2 ) ^ { n } } { 3 ^ { n } }$
Steps (b):
$a_1=\frac{(-2)^1}{3^1}=\:?$
$a_2=\frac{(-2)^2}{3^2}=\:?$
$a_3=\frac{(-2)^3}{3^3}=\:?$
$a_4=\frac{(-2)^4}{3^4}=\:?$

$a_n = \frac { ( - 2 ) ^ { n } } { 2 ^ { n } }$
Steps (c):
$a_1=\frac{(-2)^1}{2^1}=\:?$
$a_2=\frac{(-2)^2}{2^2}=\:?$
$a_3=\frac{(-2)^3}{2^3}=\:?$
$a_4=\frac{(-2)^4}{2^4}=\:?$

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