CPM Homework Help : CCA2 Problem A-83

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A-83.

For each sequence defined recursively, write the first $5$ terms and then define it explicitly.

$t(1) = 12$
$t(n + 1) = t(n) - 5$
Hint (a):
You know the first term. To find the next term, let $n = 1$ :
$t(1 + 1) = t(1) - 5$
$t(2) = 12 - 5$
Continue for $n = 2, 3, 4$ .
More Help (a):
Remember $t(0)$ will be the $y$ -intercept in the explicit equation.
Answer (a):
$12, 7, 2, -3, -8$
$t(n) = 17 - 5n$

$t(1) = 32$
$t(n + 1) =\frac { 1 } { 2 }t(n)$
Hint (b):
See part (a). This time, $t(0)$ is the initial value.
Answer (b):
$32, 16, 8, 4, 2$
$a_{n}\ =\ 64\left ( \frac{1}{2} \right )^{n}$

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