Since it is stated that there is a common ratio, the sequence is geometric.
Formula for the nth term of a geometric sequence is [tex]a_{n}=a_{1}(r)^{n-1}[/tex].
From the statement we know the following:
n = 7, [tex]a_{1}= \frac{1}{2} [/tex], r = 3
Substitute the values into the formula:
[tex]a_{7}= \frac{1}{2} (3)^{7-1}=364.5[/tex]
[tex]a_{7}=364 \frac{1}{2} = \frac{729}{2} [/tex]
