Question

Найти третий член геометрической прогрессии, если b4=18 и b7=144

Answer 1

$\left \{ {{b_{7} =144} \atop {b_{4}=18 }} \right.\\\\:\left \{ {{b_{1}*q^{6}=144} \atop {b_{1}*q^{3}=18}} \right.\\ -------\\q^{3}=8\\\\q=2\\\\b_{1} =\frac{18}{q^{3}}=\frac{18}{8}=\frac{9}{4}=2,25\\\\b_{3}=b_{1}*q^{2}=2,25*2^{2}=2,25*4=9\\\\Otvet:\boxed{b_{3}=9}$