Question

find $a_3$.\\
$a_1 = 13$\\
$a_n = a_{n - 1} + 1$\\
write your answer as an integer or fraction in simplest form.\\
$a_3 = \square$

Explanation:

Step1: Find \(a_2\)

Given \(a_1 = 13\) and the recursive formula \(a_n=a_{n - 1}+1\), to find \(a_2\), we substitute \(n = 2\) into the formula. So \(a_2=a_{2 - 1}+1=a_1 + 1\). Substituting \(a_1 = 13\), we get \(a_2=13 + 1=14\).

Step2: Find \(a_3\)

Now, to find \(a_3\), we substitute \(n = 3\) into the recursive formula \(a_n=a_{n - 1}+1\). So \(a_3=a_{3 - 1}+1=a_2 + 1\). We already found that \(a_2 = 14\), so substituting this value, we get \(a_3=14+1 = 15\).

Answer:

\(15\)