Упр.242 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) 3, 1, 1/3, …; 2) 1/4, -1/8, 1/16, …;
3) 3, v3, 1, …; 4) 5, -5v2, 10, … .

1. $$b_1=3,\quad b_2=1,\quad b_3=\frac13$$
   $$q=\frac{b_2}{b_1}=\frac13$$
   $$b_4=b_3\cdot q=\frac13\cdot\frac13=\frac19$$
   $$b_5=b_4\cdot q=\frac19\cdot\frac13=\frac1{27}$$
2. $$b_1=\frac14,\quad b_2=-\frac18,\quad b_3=\frac1{16}$$
   $$q=\frac{b_2}{b_1}=-\frac18:\frac14=-\frac12$$
   $$b_4=b_3\cdot q=\frac1{16}\cdot\left(-\frac12\right)=-\frac1{32}$$
   $$b_5=b_4\cdot q=-\frac1{32}\cdot\left(-\frac12\right)=\frac1{64}$$
3. $$b_1=3,\quad b_2=\sqrt3,\quad b_3=1$$
   $$q=\frac{b_2}{b_1}=\frac{\sqrt3}{3}=\frac1{\sqrt3}$$
   $$b_4=b_3\cdot q=1\cdot\frac1{\sqrt3}=\frac1{\sqrt3}$$
   $$b_5=b_4\cdot q=\frac1{\sqrt3}\cdot\frac1{\sqrt3}=\frac13$$
4. $$b_1=5,\quad b_2=-5\sqrt2,\quad b_3=10$$
   $$q=\frac{b_2}{b_1}=\frac{-5\sqrt2}{5}=-\sqrt2$$
   $$b_4=b_3\cdot q=10\cdot(-\sqrt2)=-10\sqrt2$$
   $$b_5=b_4\cdot q=-10\sqrt2\cdot(-\sqrt2)=20$$

Ответ

1) $$q=\frac13,\quad b_4=\frac19,\quad b_5=\frac1{27}$$

2) $$q=-\frac12,\quad b_4=-\frac1{32},\quad b_5=\frac1{64}$$

3) $$q=\frac1{\sqrt3},\quad b_4=\frac1{\sqrt3},\quad b_5=\frac13$$

4) $$q=-\sqrt2,\quad b_4=-10\sqrt2,\quad b_5=20$$