Question

find $a_2$ and $a_3$.
$a_1 = 3$
$a_n = 7a_{n - 1}$
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 \(a_n = 7a_{n - 1}\) with \(n = 2\). This means we substitute \(n = 2\) into the formula, so we need to find \(a_2=7a_{2 - 1}=7a_1\). We know that \(a_1 = 3\), so we substitute \(a_1\) into the equation: \(a_2=7\times3 = 21\).

Step2: Find \(a_3\)

To find \(a_3\), we use the recursive formula \(a_n = 7a_{n - 1}\) with \(n=3\). This gives us \(a_3 = 7a_{3 - 1}=7a_2\). We already found that \(a_2 = 21\), so we substitute \(a_2\) into the equation: \(a_3=7\times21=147\).

Answer:

\(a_2 = 21\)
\(a_3 = 147\)