Question

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

Answer 1

$(a_n)^2=(a_{n-1})\cdot(a_{n+1}),\quad{n}\in\mathbb{N}\quad\land\quad{n}\geq2\\\\(a_2)^2=(a_{1})\cdot(a_{3})\\\\x^2=\dfrac{1}{2}\cdot\dfrac{9}{8}\\\\x=\sqrt{\dfrac{9}{16}}\\\\\\\boxed{x=\dfrac{3}{4}}$