Question

find $a_2$ and $a_3$.

$a_1 = -3$
$a_n = a_{n - 1} - 13$

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 \(a_n = a_{n - 1}-13\) with \(n = 2\). So we substitute \(n = 2\) into the formula, which gives \(a_2=a_{2 - 1}-13=a_1 - 13\). We know that \(a_1=-3\), so we substitute \(a_1=-3\) into the equation: \(a_2=-3 - 13\).
\[a_2=-16\]

Step2: Find \(a_3\)

To find \(a_3\), we use the recursive formula \(a_n=a_{n - 1}-13\) with \(n = 3\). So we substitute \(n = 3\) into the formula, which gives \(a_3=a_{3 - 1}-13=a_2-13\). We already found that \(a_2 = - 16\), so we substitute \(a_2=-16\) into the equation: \(a_3=-16-13\).
\[a_3=-29\]

Answer:

\(a_2=-16\)
\(a_3=-29\)