We want to find the equation for the nth term and the value of the sixth term of the given geometric sequence. First we will find its explicit rule. Let's start by calculating the common ratio using the four terms given in the table, -192,48,-12, and 3.
We will now use the common ratio -41 and the first term -192 to write the explicit rule.
Finally, to calculate the value of a6 we will substitute 6 for n in our rule.