<PRE><B>Question 1204480</B>
&lt;br&gt;
Tutor @josgarithmetic has the right answer immediately... but in trying to check her result she does some sloppy algebra, arriving at a contradiction.&lt;br&gt;
In a geometric progression, the square of any term is equal to the product of the two terms on either side of it.  Using that fact, we get the answer immediately:&lt;br&gt;
1^2 = (M)(N)
MN = 1&lt;br&gt;
ANSWER: MN = 1&lt;br&gt;
The problem doesn&#39;t ask us to find M and N; but we can easily.&lt;br&gt;
M^2 = (4/3)(1)
M^2 = 4/3
M = 2/sqrt(3)&lt;br&gt;
That gives us sqrt(3)/2 as the common ratio; and that gives us N = sqrt(3)/2.&lt;br&gt;
The terms of the GP are 4/3, M=2/sqrt(3), 1, and N=sqrt(3)/2.&lt;br&gt;
</PRE>