Explanation

The sequence $S_{n – 1} = \frac{1}{4}(S_n)$ can be read as “to get any term in sequence S, multiply the term after that term by $\frac{1}{4}$.” Since this formula is “backwards” (usually, later terms are defined with regard to previous terms), solve the formula for $S_n$:

$S_{n – 1} = \frac{1}{4}(S_n)$
$4S_{n – 1} = S_n$
$S_n = 4S_{n – 1}$

This can be read as “to get any term in sequence S, multiply the previous term by 4.”

The problem gives the first term and asks for the fourth:

-4
$S_1$	$S_2$	$S_3$	$S_4$

To get $S_2$, multiply the previous term by 4: $(4)(-4) = -16$. Continue this procedure to find each subsequent term. Therefore, $S_3 = (4)(-16) = -64$. $S_4 = (4)(-64) = -256$:

-4	-16	-64	-256
$S_1$	$S_2$	$S_3$	$S_4$