Jeff Miller

GMAT OFFICIAL GUIDE PS – A sequence of numbers a1,a2,a3,…. is defined as follows: a1 = 3, a2 = 5…

A sequence of numbers a1,a2,a3,…. is defined as follows: a1 = 3, a2 = 5…

Solution:

We are given a sequence in which every term in the sequence after a2 is the product of all terms in the sequence preceding it. So:

a(n+1) = a(n) x a(n-1) x … x a(2) x a(1)

By the same reasoning, we have:

a(n) = a(n-1) x a(n-2) x … x a(2) x a(1)

We can substitute a(n-1) x… x a(2) x a(1) in the a(n+1) equation for a(n), so we have a(n+1) = a(n) x a(n).

However, recall that a(n) = t, so a(n+1) = t x t = t^2. By the same reasoning, we have:

a(n+2) = a(n+1) x a(n) x a(n-1) x … x a(2) x a(1)

However, a(n) x a(n-1) x …. x a(2) x a(1) = a(n+1) and a(n+1) = t^2, so:

a(n+2) = a(n+1) x a(n+1) = t^2 x t^2 = t^4

Answer: D

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