\[\boxed{\text{870\ (870).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Вероятность\ того,\ что\ решка\ \]
\[выпадет\ на\ одной\ монете,\ \]
\[равна\ \frac{1}{2}.\]
\[Найдем\ вероятность\ того,\ \]
\[что\ на\ всех\ монетах\ выпадет\ \]
\[решка:\]
\[P = \left( \frac{1}{2} \right)^{3} = \frac{1}{8}.\]
\[\boxed{\text{870.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[a_{4} = a_{3} + d = a_{2} + 2d =\]
\[= a_{1} + 3d,\]
\[d - разность\ арифметической\ \]
\[прогрессии.\]
\[По\ условию:\]
\[a_{4} = a_{1}^{2} + a_{2}^{2} + a_{3}^{2}.\]
\[a_{2} + 2d =\]
\[= a_{2}^{2} + \left( a_{2} - d \right)^{2} + \left( a_{2} + d \right)^{2}\]
\[3a_{2}^{2} + 2d^{2} - a_{2} - 2d = 0\]
\[2d^{2} - 2d + \left( 3a_{2}^{2} - a_{2} \right) = 0\]
\[D = 4 - 4 \cdot 2 \cdot \left( 3a_{2}^{2} - a_{2} \right) =\]
\[= 4 - 24a_{2}^{2} + 8a_{2} \Longrightarrow D \geq 0,\]
\[6a_{2}^{2} - 2a_{2} - 1 \leq 0\]
\[D = 4 + 24 = 28,\]
\[a_{2} = \frac{2 \pm \sqrt{28}}{12} = \frac{1 \pm \sqrt{7}}{6},\]
\[\frac{1 - \sqrt{7}}{6} \leq a_{2} \leq \frac{1 + \sqrt{7}}{6} \Longrightarrow a_{2} =\]
\[= 0 - так\ как\ целое\ число.\]
\[2d^{2} - 2d = 0\]
\[d(d - 1) = 0\]
\[d = 0 \Longrightarrow не\ подходит\ \]
\[по\ условию.\]
\[d = 1.\]
\[a_{1} = a_{2} - d = - 1\]
\[a_{2} = 0\]
\[a_{3} = a_{2} + d = 1\]
\[a_{4} = a_{2} + 2d = 2\]
\[a_{4} = a_{1}^{2} + a_{2}^{2} + a_{3}^{2} \Longrightarrow 2 =\]
\[= ( - 1)^{2} + 0^{2} + 1^{2} \Longrightarrow верно.\]
\[Ответ:a_{1} = - 1,\ a_{2} = 0,\ a_{3} = 1,\ \]
\[a_{4} = 2.\]