In a sequence of eleven real numbers, only two are shown, product of any 3 successive boxes is 120. Find the sum of all?

Question

In a sequence of eleven real numbers, only two are shown. The product of every 3 successive boxes is 120. Find the sum of all the numbers in the boxes (including the two already open).

_  _  (6)  _  _  _  _  _  _  (-4) _ 

Answer 1

-18

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Eleven numbers are: x1 to x11
x1*x2*x3=120, x2*x3*x4=120, x3*x4*x5=120 => every 3 numbers repeat in this sequence as:
x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2
As 2 numbers are given the three repeated numbers will be -4, -5, 6
The sum of eleven numbers will be equal to 4*(x1+x2+x3)-x3=4*(-3)-6=-18