ГДЗ по математике 5 класс Мерзляк ФГОС Задание 297

\[\boxed{\mathbf{297}.\ }\]

\[S = (n + 1) \cdot n\ :2.\]

\[1)\ n = 15:\]

\[S = (1 + 15) \cdot 15\ :2 =\]

\[= 16 \cdot 15\ :2 = 8 \cdot 15 = 120.\]

\[= 10 \cdot 5 + 20 + 25 + 25 =\]

\[= 70 + 50 = 120.\]

\[Верно.\]

\[2)\ n = 20:\]

\[S = (1 + 20) \cdot 20\ :2 = 21 \cdot 10 =\]

\[= 210.\]

\[= 55 + 30 \cdot 4 + 35 =\]

\[= 90 + 120 = 210.\]

\[Верно.\]

\[3)\ n = 30:\]

\[S = (1 + 30) \cdot 30\ :2 =\]

\[= 31 \cdot 30\ :2 = 930\ :2 = 465.\]

\[= 210 + 50 \cdot 4 + 55 =\]

\[= 265 + 200 = 465.\]

\[Верно.\]