Given: \(t_n=\frac{t_{n−1}}{t_{n−2}}\)

\(t_1=3\)
\(t_2=5\)

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

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

\(t_5=\frac{1}{5} \)

\(t_6=\frac{3}{5} \)

\(t_7=3 \)

\(t_8=5\)
.
.
.
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