Найти сумму первых 24 членов арифметической прогрессии, если a_n=3/4*n-5/8.

\[a_{n} = \frac{3}{4}n - \frac{5}{8}\]

\[a_{1} = \frac{3^{\backslash 2}}{4} - \frac{5}{8} = \frac{6}{8} - \frac{5}{8} = \frac{1}{8};\]

\[a_{24} = \frac{3}{4} \cdot 24 - \frac{5}{8} = 18 - \frac{5}{8} = 17\frac{3}{8}.\]

\[S_{24} = \frac{\left( a_{1} + a_{24} \right)}{2} \cdot 24 =\]

\[= \left( \frac{1}{8} + 17\frac{3}{8} \right) \cdot 12 = 17\frac{4}{8} \cdot 12 =\]

\[= 17\frac{1}{2} \cdot 12 = \frac{35}{2} \cdot 12 =\]

\[= 35 \cdot 6 = 210.\]

\[Ответ:210.\]