Question

I need help with the table. this is college math

Answer 1

ANSWER:

First blank = 8

Second blank = 384

SOLUTION:

This series follows the geometric series

$a_m=a_0r^m$

Using the given values, we can solve for the value of r

$\begin{gathered} 12=6r^1 \\ r\text{ = 2} \end{gathered}$

Substitute this to the equation

$\begin{gathered} 1536=6(2)^m \\ 256=2^m \\ \log \text{ 256 = m log 2} \\ \frac{\log \text{ 256}}{\log \text{ 2}}\text{ = m} \\ m\text{ = 8} \end{gathered}$

For the second blank

$a_6=6(2)^6=384$