Question

find $a_2$, $a_3$, and $a_4$.
$a_1 = 56$
$a_n = \frac{1}{2}a_{n - 1}$
write your answers as integers or fractions in simplest form.
$a_2 = $
$a_3 = $
$a_4 = $

Explanation:

Step1: Calculate $a_2$ using $a_1$

Substitute $n=2$, $a_1=56$ into $a_n=\frac{1}{2}a_{n-1}$
$a_2 = \frac{1}{2}a_1 = \frac{1}{2} \times 56 = 28$

Step2: Calculate $a_3$ using $a_2$

Substitute $n=3$, $a_2=28$ into $a_n=\frac{1}{2}a_{n-1}$
$a_3 = \frac{1}{2}a_2 = \frac{1}{2} \times 28 = 14$

Step3: Calculate $a_4$ using $a_3$

Substitute $n=4$, $a_3=14$ into $a_n=\frac{1}{2}a_{n-1}$
$a_4 = \frac{1}{2}a_3 = \frac{1}{2} \times 14 = 7$

Answer:

$a_2 = 28$
$a_3 = 14$
$a_4 = 7$