Answer
Thus, the general formula for the given sequence is:
$a_n=21 (\dfrac{1}{3})^{n-1}$
Work Step by Step
The $n^{th}$ term of a geometric sequence is given by the formula:
$ a_n=a_1r^{n-1}$
where $r$=common ratio and $a_1$= the first term
The common ratio of a geometric sequence is equal to the quotient (ratio) of any term and the term before it:
$ \ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}$
Here $a_2=7$ and $r=\dfrac{1}{3}$
So, $a_2=a_1r^{2-1}=7\\a_1\cdot(\dfrac{1}{3})^1=7\\a_1=21$
Thus, the general formula for the given sequence is:
$a_n=21 (\dfrac{1}{3})^{n-1}$
