Exercise 60 Page 280

Let's start by considering the given recursive formula for the arithmetic sequence. To find the second, third, and fourth terms, we will substitute $2,$ $3,$ and $4$ in the above formula. To do so, we will use a table.

$n$	$A(n)=A(n-1)-4$	$A(n)$
$1$	$A(1)=8$
$2$	$A(2)=A(2-1)-4$	$A(2)=A(1)-4$ $\Updownarrow$ $A(2)=8-4=4$
$3$	$A(3)=A(3-1)-4$	$A(3)=A(2)-4$ $\Updownarrow$ $A(3)=4-4=0$
$4$	$A(4)=A(4-1)-4$	$A(4)=A(3)-4$ $\Updownarrow$ $A(4)=0-4=\text{-}4$

Therefore, the next three terms of the sequence are $4,$ $0,$ and $\text{-}4.$ We also want to find the explicit formula of this arithmetic sequence. It combines the information provided by the two equations of the recursive form into a single equation. In these formulas, $d$ is the common difference and $A(1)$ is the first term. Looking once again at the given recursive formula, we can identify the common difference $d$ and the value of the first term $A_1.$ We can see that the common difference is $\text{-}4$ and the first term is $8.$ Now we have enough information to write an explicit formula for this sequence.