В арифметической прогрессии a_4=26; a_8=68. Найдите a_21.

Ответ:

\[a_{4} = 26;\ \ a_{8} = 68;\]

\[a_{21} = a_{1} + 20d;\]

\[a_{4} = a_{1} + 3d;a_{1} = a_{4} - 3d;\]

\[a_{8} = a_{1} + 7d;a_{1} = a_{8} - 7d;\]

\[a_{4} - 3d = a_{8} - 7d\]

\[26 - 3d = 68 - 7d\]

\[4d = 42\]

\[d = 10,5.\]

\[a_{1} = a_{4} - 3d = 26 - 3 \cdot 10,5 =\]

\[= 26 - 31,5 = - 5,5.\]

\[a_{21} = - 5,5 + 20 \cdot 10,5 =\]

\[= - 5,5 + 210 = 204,5.\]

\[Ответ:204,5.\]