Question

find $a_4$.\\
$a_1 = 2$\\
$a_n = 4a_{n - 1}$\\
write your answer as an integer or fraction in simplest form.\\
\\
$a_4 = \square$

Explanation:

Step1: Find \(a_2\)

Given \(a_1 = 2\) and \(a_n = 4a_{n - 1}\), for \(n = 2\), we have \(a_2 = 4a_1\). Substituting \(a_1 = 2\), we get \(a_2 = 4\times2 = 8\).

Step2: Find \(a_3\)

For \(n = 3\), using the formula \(a_n = 4a_{n - 1}\), we have \(a_3 = 4a_2\). Substituting \(a_2 = 8\), we get \(a_3 = 4\times8 = 32\).

Step3: Find \(a_4\)

For \(n = 4\), using the formula \(a_n = 4a_{n - 1}\), we have \(a_4 = 4a_3\). Substituting \(a_3 = 32\), we get \(a_4 = 4\times32 = 128\).

Answer:

\(128\)