Question

determine o valo de x nas sequencias abaixo, após calcule a razão q e classifique as P.G´s
a) 4x, 2x+3, x+5

b) x-1, 2x+1, 4x

Answer 1

$\boxed{\mathsf{q=\frac{a_{n}}{a_{(n-1)}}}} \\ \\ \frac{a_{2}}{a_{1}} = \frac{ a_{3} }{ a_{2} } \\ \\ (a_{2})^{2} = a_{1} * a_{2}$

a)

$(2x +3)^{2} = (4x) * (x+5)\\4x^{2} +12x +9 = 4x^{2} +20x\\9 = 20x -12x = \frac{9}{8}$

q = (2 * 9/8 + 3)/(4 * 9/8)

q = 9/4 * 2/9

q = 1/2 → Decrescente

b)

$(2x+1)^{2} =(x-1)*(4x)\\ 4x^{2} +4x +1 = 4x^{2} -4x\\ 4x +4x = -1 \\ x = -\frac{1}{8}$

q = (-2/8 +1)/(-1/8 -1)

q = (3/4) * (-8/9)

q = -2/3 → Crescente \ Oscilante