Question

У геометричній прогресії : b4=24, b7=192. Знайти b9

Answer 1

$\displaystyle\bf\\\left \{ {{b_{7} }=192\atop {b_{4} }=24} \right. \\\\\\:\left \{ {{b_{1} \cdot q^{6}=192 } \atop {b_{1} \cdot q^{3} =24}} \right.\\---------\\q^{3}=8\\\\q=\sqrt[3]{8}=2\\\\b_{1} =24: q^{3}=24:8=3\\\\b_{9} =b_{1} \cdot q^{8}=3\cdot 256=768\\\\Otvet \ : \ b_{9} =768$