\[\boxed{\text{623}\text{\ (623)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ b_{1} = 6;\ \ q = 2:\ \ \]
\[b_{2} = b_{1} \cdot q = 6 \cdot 2 = 12,\ \ \]
\[b_{3} = b_{2} \cdot q = 12 \cdot 2 = 24,\ \ \]
\[b_{4} = b_{3} \cdot q = 24 \cdot 2 = 48,\ \ \]
\[b_{5} = b_{4} \cdot q = 48 \cdot 2 = 96.\]
\[\textbf{б)}\ b_{1} = - 16;\ \ q = \frac{1}{2}:\]
\[b_{2} = b_{1} \cdot q = - 16 \cdot \frac{1}{2} = - 8,\ \ \]
\[b_{3} = b_{2} \cdot q = - 8 \cdot \frac{1}{2} = - 4,\ \ \]
\[b_{4} = b_{3} \cdot q = - 4 \cdot \frac{1}{2} = - 2,\ \ \]
\[b_{5} = b_{4} \cdot q = - 2 \cdot \frac{1}{2} = - 1\text{.\ }\]
\[\textbf{в)}\ \ b_{1} = - 24;\ \ q = - 1,5:\ \]
\[b_{2} = b_{1} \cdot q = - 24 \cdot ( - 1,5) = 36,\ \ \]
\[b_{3} = b_{2} \cdot q = 36 \cdot ( - 1,5) = - 54,\ \]
\[b_{4} = b_{3} \cdot q = - 54 \cdot ( - 1,5) = 81,\ \ \]
\[b_{5} = b_{4} \cdot q = 81 \cdot ( - 1,5) = - 121,5.\]
\[\textbf{г)}\ \ b_{1} = 0,4;\ \ \ q = \sqrt{2}:\ \]
\[b_{2} = b_{1} \cdot q = 0,4 \cdot \sqrt{2},\ \ \]
\[b_{3} = b_{2} \cdot q = 0,4 \cdot \sqrt{2} \cdot \sqrt{2} = 0,8,\ \ \]
\[b_{4} = b_{3} \cdot q = 0,8\sqrt{2},\ \ \]
\[b_{5} = b_{4} \cdot q = 0,8 \cdot \sqrt{2} \cdot \sqrt{2} = 1,6.\]