Given: $t_n=\frac{t_{n−1}}{t_{n−2}}$

$t_1=3$
$t_2=5$

So, $t_3=\frac{t_{3−1}}{t_{3−2}}=\frac{t_{2}}{t_{1}}=\frac{5}{3}$

$t_4=\frac{t_{4−1}}{t_{4−2}}=\frac{t_{3}}{t_{2}}=\frac{(\frac{5}{3})}{5} =\frac{1}{3}$

$t_5=\frac{1}{5}$

$t_6=\frac{3}{5}$

$t_7=3$

$t_8=5$
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As we can see, the pattern repeats itself every 6 terms.
Also notice that the product of the first six terms is 1.
This means the product of the NEXT six terms must also be 1
And the product of the six terms AFTER THAN must be 1 as well

The first 54 terms will consist of nine groups consisting of 6 terms each.
So, the product of the first 54 terms will equal the product of nine 1's
So, the product must equal 1

Answer: C

Cheers,
Brent