Question

find $a_2$ and $a_3$.

$a_1 = 14$
$a_n = a_{n - 1} - 4$

write your answers as integers or fractions in simplest form.

$a_2 = \square$
$a_3 = \square$

Explanation:

Step1: Find \( a_2 \)

To find \( a_2 \), we use the recursive formula \( a_n = a_{n - 1}-4 \) with \( n = 2 \). So we substitute \( a_1 = 14 \) into the formula:
\( a_2=a_{2 - 1}-4=a_1 - 4 \)
Substituting \( a_1 = 14 \), we get \( a_2=14 - 4=10 \)

Step2: Find \( a_3 \)

To find \( a_3 \), we use the recursive formula \( a_n = a_{n - 1}-4 \) with \( n = 3 \). So we substitute \( a_2 = 10 \) into the formula:
\( a_3=a_{3 - 1}-4=a_2 - 4 \)
Substituting \( a_2 = 10 \), we get \( a_3=10 - 4 = 6 \)

Answer:

\( a_2=\boldsymbol{10} \)
\( a_3=\boldsymbol{6} \)