\[\boxed{\text{702\ (702).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ x_{1} + 1;x_{2} + 1;\ldots;x_{n} + 1;\ldots;\]
\[c_{1} = x_{1} + 1,\ \ \]
\[c_{n} = x_{n} + 1 = x_{n} \cdot q^{n} + 1,\ \]
\[q = \frac{c_{n}}{c_{n - 1}} = \frac{x_{n} \cdot q^{n} + 1}{x_{n - 1} \cdot q^{n - 1} + 1} \Longrightarrow\]
\[\Longrightarrow зависит\ от\ n \Longrightarrow не\ \]
\[геометрическая\ прогрессия.\]
\[\textbf{б)}\ 3x_{1};3x_{2};\ldots;3x_{n};\ldots;\]
\[c_{1} = 3x_{1},\ \ c_{n} = 3x_{n},\ \ \]
\[\frac{c_{n}}{c_{n - 1}} = \frac{3x_{n}}{3x_{n - 1}} =\]
\[= q \Longrightarrow геометрическая\ \]
\[прогрессия.\]
\[\textbf{в)}\ x_{1}^{2};x_{2}^{2};\ldots;x_{n}^{2};\ldots;\]
\[c_{1} = x_{1}^{2},\ \ c_{n} = x_{n}^{2},\ \ \]
\[\frac{c_{n}}{c_{n - 1}} = \frac{x_{n}^{2}}{x_{(n - 1)}^{2}} =\]
\[= q^{2} \Longrightarrow геометрическая\ \]
\[прогресссия.\]
\[\textbf{г)}\frac{1}{x_{1}};\frac{1}{x_{2}};\ldots;\frac{1}{x_{n}};\ldots;\ \]
\[c_{1} = \frac{1}{x_{1}},\ \ c_{n} = \frac{1}{x_{n}} = \frac{1}{c_{1}q^{n - 1}},\ \ \]
\[\frac{c_{n}}{c_{n - 1}} = \frac{1}{c_{1}q^{n - 1}} \cdot c_{1}q^{n - 2} =\]
\[= q^{- 1} \Longrightarrow геометрическая\ \]
\[прогресссия.\]