Question

O valor positivo de x que torna a sucessão (1/2, x, 9/8) uma pg ?

Answer 1

$P.G.=\left(\dfrac{1}{2};\ x;\ \dfrac{9}{8}\right)\\\\\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}\\\\\\(a_2)^2=a_1\cdot{a}_3\\\\\\(x)^2=\left(\dfrac{1}{2}\right)\cdot\left(\dfrac{9}{8}\right)\\\\\\x^2=\dfrac{9}{16}\\\\\\x=\pm\sqrt{\dfrac{9}{16}}\quad\text{Neste caso considera-se apenas o valor positivo}\\\\\\\boxed{x=\dfrac{3}{4}}\\\\\\\\P.G.=\left(\dfrac{1}{2};\ \dfrac{3}{4};\ \dfrac{9}{8}\right)$