Question

Допоможіть будь-ласка​

Answer 1

Ответ:

а) $-3.$

б) $-2.$

Объяснение:

а) $a_3 = 16,\ a_7 = 4;\\16 = a_1 + 2d\ \ \wedge\ \ 4 = a_1 + 6d;\\\left \{ \\{{16 = a_1 + 2d;}\\\atop\\{4 = a_1 + 6d.}} \right. \Rightarrow\left \{ \\{{d = \frac{16 - a_1}{2}};\\\atop\\{d = \frac{4 - a_1}{6}}.} \right.\\\\\frac{16-a_1}{2} = \frac{4 - a_1}{6};\\\\16 - a_1 = \frac{4 - a_1}{3};\\48 - 3a_1 = 4 - a_1;\\\\-2a_1 = 44;\\a_1 = -22;\\\\ d = \frac{16-22}{2} = -\frac{6}{2} = -3.$

б) $a_4 = 10,\ a_{21} = -24;\\10 = a_1 + 3d\ \ \wedge\ \ -24 = a_1 + 20d;\\\left \{ \\{{10 = a_1 + 3d;}\\\atop\\{-24 = a_1 + 20d.}} \right. \Rightarrow\left \{ \\{{d = \frac{10 - a_1}{3}};\\\atop\\{d = -\frac{24 + a_1}{20}}.} \right.\\\\\frac{10-a_1}{3} = -\frac{24 + a_1}{20};\\\\10 - a_1 = -\frac{72 + 3a_1}{20};\\200 - 20a_1 = -72 - 3a_1;\\\\17a_1 = 272;\\a_1 = 16;\\\\ d = \frac{10-16}{3} = -\frac{6}{3} = -2.$