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 \(a_4=(a1)(a2)(a3).\) 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

Source: Official Guide

## 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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Let's list a few terms....VJesus12 wrote: ↑Fri Jan 28, 2022 7:24 amA 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 \(a_4=(a1)(a2)(a3).\) 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

Source: Official Guide

term1 = 3

term2 = 5

term3 = (term2)(term1) = (5)(3) = 15 (term2)(term1)

term4 = (term3)(term2)(term1) = (15)(5)(3) = 15²

term5 = (term4)(term3)(term2)(term1) = (15²)(15)(5)(3) =

**15⁴**

term6 = (term5)(term4)(term3)(term2)(term1) = (

**15⁴**)(15²)(15)(5)(3) =

**15⁸**

At this point, we can see the pattern.

Continuing, we get....

term7 = 15^16

term8 = 15^32

**Each term in the sequence is equal to the SQUARE of term before it**

**If term_n =t and n > 2, what is the value of term_n+2 in terms of t?**So, term_n = t

term_n+1 = t²

term_n+2 = t⁴

Answer: D

Cheers,

Brent