Задание 4................

{ $b_n$ } - геометрическая прогрессия
$b_5=8$
$b_9=\frac{8}{81}$
$b_5=b_1*q^4$
$b_9=b_1*q^8$

$\left \{ {{b_1q^4=8} \atop {b_1*q^8= \frac{8}{81} }} \right.$

$\left \{ {{b_1q^4=8} \atop {b_1*q^4*q^4= \frac{8}{81} }} \right.$

$\left \{ {{b_1q^4=8} \atop {8*q^4= \frac{8}{81} }} \right.$

$\left \{ {{b_1q^4=8} \atop {q^4= \frac{1}{81} }} \right.$

$q^4= \frac{1}{81}$
$q=б \frac{1}{3}$
1)
$q= \frac{1}{3}$
$b_1= \frac{8}{q^4} = 8: \frac{1}{81}=8*81=648$

$b_7=b_1*q^6=648* (\frac{1}{3} )^6=3*(2*3)^3* (\frac{1}{3} )^6=3^4*8* \frac{1}{3^6}= \frac{8}{9}$

2)
$q=- \frac{1}{3}$
$b_1= \frac{8}{q^4} = 8: \frac{1}{81}=8*81=648$
$b_7=b_1*q^6=648* (-\frac{1}{3} )^6=3*(2*3)^3* (-\frac{1}{3} )^6=3^4*8* \frac{1}{3^6}= \frac{8}{9}$

Ответ: $\frac{8}{9}$