Question

Найдите знаменатель геометрической прогрессии если c6 = 25, c8= 4
С решением .

Answer 1

$c_{6}=c_{1}*q^5\c_{8}=c_{1}*q^7\\ left { {{25=c_{1}*q^5} atop {4=c_{1}*q^7}} right. = textgreater Razdelim-2yr-na-1= textgreater \\= textgreater left { {{25=c_{1}*q^5} atop {frac{4}{25}=q^2}} right.left { {{25=c_{1}*q^5} atop {+-frac{2}{5}=q}} right.\\Ordelno-reshaem-pervoe-yravnenie\1)25=c_{1}*(frac{2}{5})^5\\25=c_{1}*frac{32}{3125}\\c_{1}=frac{25}{frac{32}{3125}}\\c_{1}=frac{25*3125}{32}\\c_{1}=frac{78125}{32}\\c_{1}=2441frac{13}{32}$
$2)25=c_{1}*(frac{-2}{5})^5\\25=c_{1}*(-frac{32}{3125})\\c_{1}=frac{25}{frac{-32}{3125}}\\c_{1}=frac{25*3125}{-32}\\c_{1}=-frac{78125}{32}\\c_{1}=-2441frac{13}{32}$
Вернемся в систему, и получим две пары решений
$1. left { {{c_1}=2441frac{13}{32}Ї} atop {q=frac{2}{5}}} right. 2. left { {{c_1}=-2441frac{13}{32}Ї} atop {q=-frac{2}{5}}} right.$x]
Ответ: знаменатель прогрессии равен +-2/5