Answer
$a_n=21\cdot (\frac{1}{3})^{n-1}$
Work Step by Step
RECALL:
(1) The $n^{th}$ term $a_n$ of a geometric sequence is given by the formula:
$a_n=a_1 \cdot r^{n-1}$
where
$a_1$ = first term
$r$ = common ratio
(2) The common ratio of a geometric sequence is equal to the quotient of any term and the term before it:
$r = \dfrac{a_n}{a_{n-1}}$
Note that:
$r=\dfrac{a_2}{a_1}$
The given geometric sequence has:
$a_2=7$
$r=\frac{1}{3}$
Substitute these values into the equation involving $r$ above to obtain:
$r=\dfrac{a_2}{a_1}
\\\dfrac{1}{3} = \dfrac{7}{a_1}$
Cross-multiply to obtain:
$1(a_1)=3(7)
\\a_1=21$
Therefore, the $n^{th}$ term of the sequence is given by the formula:
$a_n= a_1 \cdot r^{n-1}
\\a_n=21\cdot (\frac{1}{3})^{n-1}$