Question

Determine o valor de x na PA (x,3/2,-2/3).

Answer 1

$\begin{matrix}(a,b,c)&(x,\dfrac{3}{2},-\dfrac{2}{3})\\\\b-a=c-b&\dfrac{3}{2}-x=-\dfrac{2}{3}-\dfrac{3}{2}\end{matrix}$

$\dfrac{3}{2}-x=-\dfrac{2}{3}-\dfrac{3}{2}~~~(\cdot6)\\\\9-6x=-4-9\\\\-6x=-22\\\\\boxed{x=\dfrac{11}{3}}$

Answer 2

b = (a + c)/2
3/2 = (x-2/3)/2
eliminando os denominadores, temos:
x-2/3 = 3
x = 3+2/3
x = 11/3