Дана арифметическая прогрессия, в которой a_6=-7,8; a_19=-10,4. Найдите a_1.

\[a_{6} = - 7,8;\ \ a_{19} = - 10,4;\]

\[a_{6} = a_{1} + 5d;\ \ a_{1} = a_{6} - 5d\]

\[a_{19} = a_{1} + 18d;\ \ a_{1} = a_{19} - 18d;\]

\[a_{6} - 5d = a_{19} - 18d\]

\[13d = a_{19} - a_{6}\]

\[13d = - 10,4 + 7,8\]

\[13d = - 2,6\]

\[d = - 2,6\ :13\]

\[d = - 0,2.\]

\[a_{1} = a_{6} - 5d =\]

\[= - 7,8 - 5 \cdot ( - 0,2) =\]

\[= - 7,8 + 1 = - 6,8.\]

\[Ответ:a_{1} = - 6,8.\]