Дана арифметическая прогрессия: a_2=-5; a_6-a_4=6. Найдите S_10.

Ответ:

\[a_{2} = - 5;\ \ a_{6} - a_{4} = 14;\]

\[a_{1} + 5d - a_{1} - 3d = 6\]

\[2d = 6\]

\[d = 3.\]

\[a_{2} = a_{1} + d\]

\[a_{1} = a_{2} - d = - 5 - 3 = - 8.\]

\[a_{10} = a_{1} + 9d = - 5 + 9 \cdot 3 =\]

\[= - 5 + 27 = 22.\]

\[S_{10} = \frac{a_{1} + a_{10}}{2} \cdot 10 =\]

\[= ( - 5 + 22) \cdot 5 = 17 \cdot 5 = 85.\]

\[Ответ:85.\]