Упр.228 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) b_2=15, b_3=25; 2) b_2=14, b_4=686, q > 0.

1. $$q=\frac{b_3}{b_2}=\frac{25}{15}=\frac{5}{3}$$

   $$b_1=\frac{b_2}{q}=15:\frac{5}{3}=9$$

   $$b_5=b_1q^4=9\cdot\left(\frac{5}{3}\right)^4=9\cdot\frac{625}{81}=\frac{625}{9}=69\frac{4}{9}$$

   $$S_4=\frac{b_1(q^4-1)}{q-1}=\frac{9\left(\left(\frac{5}{3}\right)^4-1\right)}{\frac{5}{3}-1}$$

   $$S_4=\frac{9\left(\frac{625}{81}-1\right)}{\frac{2}{3}}=\frac{9\cdot\frac{544}{81}}{\frac{2}{3}}=\frac{544}{9}\cdot\frac{3}{2}=\frac{272}{3}=90\frac{2}{3}$$

2. $$b_3=\sqrt{b_2b_4}=\sqrt{14\cdot686}=\sqrt{9604}=98$$

   $$q=\frac{b_3}{b_2}=\frac{98}{14}=7$$

   $$b_1=\frac{b_2}{q}=\frac{14}{7}=2$$

   $$b_5=b_1q^4=2\cdot7^4=2\cdot2401=4802$$

   $$S_4=\frac{b_1(q^4-1)}{q-1}=\frac{2(7^4-1)}{7-1}=\frac{2(2401-1)}{6}=800$$

Ответ

1) $$b_5=69\frac{4}{9},\quad S_4=90\frac{2}{3}$$

2) $$b_5=4802,\quad S_4=800$$