CAT 2018 Slot 1 QA Question 32: Let $x, y, z$ be three positive real numbers in a geometric progression such that $x

Question

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ratio of the geometric progres

Accepted Answer

Let the three terms of the GP be $a,ar,ar^{2}$, where $r > 1$ because $x 
Since $5x$, $16y$ and $12z$ are in AP,
$5x + 12z = 2 	imes 16y$
$5a + 12ar^{2} = 32ar$
$12r^{2} - 32r + 5 = 0$
$r = \dfrac{32 \pm 28}{24}$
$r = \dfrac{5}{2}$ or $r = \dfrac{1}{6}$
Since $r > 1$, the common ratio is $\dfrac{5}

Let x,y,zx, y, zx,y,z be three positive real numbers in a geometric progression such that x<y<zx < y < zx<y<z. If 5x5x5x, 16y16y16y, and 12z12z12z are in an arithmetic progression then the common ratio of the geometric progression is

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$ . If $5x$ , $16y$ , and $12z$ are in an arithmetic progression then the common ratio of the geometric progression is