Answer
$r=s^{2/7}$
$a_5=s^{8/7}$
The $n^{th}$ term of the geometric sequence is: $a_n=1 \cdot \left(s^{2/7}\right)^{n-1}$
Work Step by Step
RECALL:
(1) The common ratio of a geometric sequence is equal to the quotient of any two consecutive terms:
$r =\dfrac{a_n}{a_{n-1}}$
(2) The $n^{th}$ term of a geometric sequence is given by the formula:
$a_n = a\cdot r^{n-1}$
where
$a$ = first term
$r$ = common ratio
The sequence is said to be geometric.
Thus, we can proceed to solving for the common ratio:
$\require{cancel}
r=\dfrac{s^{2/7}}{1}
\\r=s^{2/7}$
The fifth term can be found by multiplying the common ratio to the fourth term.
The fourth term is $s^{6/7}$.
Thus, the fifth term is:
$a_5=s^{6/7} \cdot s^{2/7}$
Use the rule $a^m \cdot a^n = a^{m+n}$ to obtain:
$a_5=s^{6/7 + 2/7}
\\a_5=s^{8/7}$
With a first term of $1$ and a common ratio of $r=s^{2/7}$, the $n^{th}$ term of the geometric sequence is:
$a_n=a \cdot r^{n-1}
\\a_n=1 \cdot \left(s^{2/7}\right)^{n-1}$
