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# The sum of three decreasing numbers in AP is 27. If -1, -1, and 3 are added to them respectively the resulting series is in GP. The numbers are

$(a)\;17,9,1\qquad(b)\;16,9,2\qquad(c)\;13,9,5\qquad(d)\;5,9,13$

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A)
$(9+d-1)\;(9-d+3)=(9-1)^2$
$(8+d)\;(12-d)=64$
$96+4d-d^2=64$
$d^2-4d-32=0$
$(d+4)(d-8)=0$
$d=-4,8$