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Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE PS
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
