Answer
$r=5^{c}$
$a_{5}=5^{4c+1}$
$a_{n}=5^{(n-1)c+1}$
Work Step by Step
A geometric sequence is a sequence whose terms are obtained by multiplying each term by the same fixed constant $r$ to get the next term.
A geometric sequence has the form
$a, ar, ar^{2}, ar^{3}, \ldots$
The number $a$ is the first term of the sequence, and the number $r $is the common ratio.
The nth term of the sequence is $\quad a_{n}=ar^{n-1}$
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The common ratio is the ratio between any two neighboring terms:
$r=\displaystyle \frac{5^{c+1}}{5^{1}}=5^{c+1-1}=5^{c}$
The first term $a=5.$
The fifth term (n=5)
$a_{5}=5(5^{c})^{5-1}=5(5^{4c})=5^{4c+1}$
The general, nth term:
$a_{n}=5(5^{c})^{n-1}=5(5^{nc-c})=5^{nc-c+1}$
