Question

Calcule o quinto termo da PG (1/2, X, 3/4...)

Answer 1

$a3=a1.{q}^{2} \\ \frac{3}{4}=\frac{1}{2}.{q}^{2}$

${q}^{2}=\frac{3}{2}$

$a5=a3.{q}^{2} \\ a5=\frac{3}{4}. \frac{3}{2}$

$\frac{9}{8}$

Answer 2

Resposta:

O 5° termo vale 9/8.

Explicação passo-a-passo:

a1 = ½

n = 5

Cálculo de x:

$\frac{x}{ \frac{1}{2} } = \frac{ \frac{3}{4} }{x} \\ {x}^{2} = \frac{1}{2} \times \frac{3}{4} \\ {x}^{2} = \frac{3}{8} \\ x = \sqrt{ \frac{3}{8} } \\ x = \frac{ \sqrt{3} }{2 \sqrt{2} } \\ x = \frac{ \sqrt{6} }{4}$

Cálculo da razão:

$q = \frac{3}{4} \div \frac{ \sqrt{6} }{4} \\ q = \frac{3}{4} \times \frac{4}{ \sqrt{6} } \\ q = \frac{3}{ \sqrt{6} } \\ q = \frac{3 \sqrt{6} }{6} \\ q = \frac{ \sqrt{6} }{2}$

$a_5 = a_1.q^{n-1}$

$a_5 = a_1. {q}^{n - 1} \\ a_5 = \frac{1}{2} . {( \frac{ \sqrt{6} }{2} )}^{5 - 1} \\ a_5 = \frac{1}{2} . {( \frac{ \sqrt{6} }{2} )}^{4} \\ a_5 = \frac{1}{2} . \frac{ \sqrt{1296} }{16} \\ a_5 = \frac{1}{2} . \frac{36}{16} \\ a_5 = \frac{18}{16} \\ a_5 = \frac{9}{8}$