Question

Задание 4................

Answer 1

{$b_n$} - 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: $frac{8}{9}$