Упр.15.25 ГДЗ Мордкович Александрова 9 класс (Алгебра)

а) xn=(-2)n;
б) cn= (-1)n+1-(-1)n;
в) bn=2(-3)n-1;
г) dn=(-2)n+(-2)n-1.

1. $$x_n = (-2)^n$$

   $$x_1 = (-2)^1 = -2$$
   
   $$x_2 = (-2)^2 = 4$$
   
   $$x_3 = (-2)^3 = -8$$
   
   $$x_4 = (-2)^4 = 16$$
   
   $$x_5 = (-2)^5 = -32$$

2. $$c_n = (-1)^{n+1} — (-1)^n$$

   $$c_1 = (-1)^2 — (-1)^1 = 1 — (-1) = 2$$
   
   $$c_2 = (-1)^3 — (-1)^2 = -1 — 1 = -2$$
   
   $$c_3 = (-1)^4 — (-1)^3 = 1 — (-1) = 2$$
   
   $$c_4 = (-1)^5 — (-1)^4 = -1 — 1 = -2$$
   
   $$c_5 = (-1)^6 — (-1)^5 = 1 — (-1) = 2$$

3. $$b_n = 2 \cdot (-3)^{n-1}$$

   $$b_1 = 2 \cdot (-3)^0 = 2$$
   
   $$b_2 = 2 \cdot (-3)^1 = -6$$
   
   $$b_3 = 2 \cdot (-3)^2 = 18$$
   
   $$b_4 = 2 \cdot (-3)^3 = -54$$
   
   $$b_5 = 2 \cdot (-3)^4 = 162$$

4. $$d_n = (-2)^n + (-2)^{n-1}$$

   $$d_1 = (-2)^1 + (-2)^0 = -2 + 1 = -1$$
   
   $$d_2 = (-2)^2 + (-2)^1 = 4 + (-2) = 2$$
   
   $$d_3 = (-2)^3 + (-2)^2 = -8 + 4 = -4$$
   
   $$d_4 = (-2)^4 + (-2)^3 = 16 + (-8) = 8$$
   
   $$d_5 = (-2)^5 + (-2)^4 = -32 + 16 = -16$$

Ответ

а) $$-2,\ 4,\ -8,\ 16,\ -32$$;
б) $$2,\ -2,\ 2,\ -2,\ 2$$;
в) $$2,\ -6,\ 18,\ -54,\ 162$$;
г) $$-1,\ 2,\ -4,\ 8,\ -16$$.