Question 1141127
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Since a, b, c, and d are in geometric progression, call them a, ar, ar^2, and ar^3.  Then you need to show that (a+ar)^2, (ar+ar^2)^2, and (ar^2+ar^3)^2 are in geometric progression.  That is almost obvious.<br>
{{{(ar+ar^2)^2 = (r(a+ar))^2 = r^2(a+ar)^2}}}  -->  The second term is r^2 times the first.<br>
{{{(ar^2+ar^3)^2 = (r^2(a+ar))^2 = r^4(a+ar)^2}}}  -->  The third term is r^4 = (r^2)^2 times the first.<br>
The common ratio between the terms of the new sequence is r^2.