We want to find the equation for the nth term and the value of the sixth term of the given . First we will find its . Let's start by calculating the using the four terms given in the graph, 224, 112, 56, and 28.
We will now use the common ratio
21 and the first term
224 to write the explicit rule.
an=a1⋅rn−1⇔an=224(21)n−1
Finally, to calculate the value of
a6 we will substitute
6 for
n in our rule.
an=224(21)n−1 a6=224(21)6−1 a6=224(21)5 a6=224(321) a6=32224