Question

find $a_2$ and $a_3$.

$a_1 = -7$
$a_n = a_{n - 1} + 1$

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 \(a_n = a_{n - 1}+1\) with \(n = 2\). So we substitute \(n = 2\) into the formula, which gives \(a_2=a_{2 - 1}+1=a_1 + 1\). We know that \(a_1=-7\), so we substitute \(a_1=-7\) into the equation: \(a_2=-7 + 1=-6\).

Step2: Find \(a_3\)

To find \(a_3\), we use the recursive formula \(a_n=a_{n - 1}+1\) with \(n = 3\). Substituting \(n = 3\) into the formula, we get \(a_3=a_{3 - 1}+1=a_2+1\). We already found that \(a_2=-6\), so we substitute \(a_2 = - 6\) into the equation: \(a_3=-6 + 1=-5\).

Answer:

\(a_2=-6\)
\(a_3=-5\)