A sequence of numbers \(a_1, a_2, a_3,\ldots\) is defined as follows: \(a_1=3, a_2=5,\) and every term in the sequence

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A sequence of numbers \(a_1, a_2, a_3,\ldots\) is defined as follows: \(a_1=3, a_2=5,\) and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3=(a_1)(a_2)\) and \(a_4=(a_1)(a_2)(a_3).\) If \(a_n=t\) and \(n>2,\) what is the value of \(a_{n+2}\) in terms of \(t?\)

(A) \(4t\)
(B) \(t^2\)
(C) \(t^3\)
(D) \(t^4\)
(E) \(t^8\)

Answer: D

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