Home > CCA2 > Chapter A > Lesson A.2.3 > ProblemA-83

A-83.

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

1. $t(1) = 12$
$t(n + 1) = t(n) - 5$

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 $n = 2, 3, 4$.

Remember $t(0)$ will be the $y$-intercept in the explicit equation.

$12, 7, 2, -3, -8$
$t(n) = 17 - 5n$

1. $t(1) = 32$
$t(n + 1) =\frac { 1 } { 2 }t(n)$

See part (a). This time, $t(0)$ is the initial value.

$32, 16, 8, 4, 2$
$a_{n}\ =\ 64\left ( \frac{1}{2} \right )^{n}$