Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 651

а) 2/3; 3/4; ...
a₁ = 2/3
a₂ = 3/4
d = a₂ – a₁ = 3/4 – 2/3 = 9 – 8/12 = 1/12

S_n = $$\frac{2a_1 + d(n - 1)}{2}$$ · n

S₁₀ = $$\frac{2 · \frac{2}{3} + \frac{1}{12} · (10 - 1)}{2}$$ · 10 = (4/3 + 1/12 · 9) · 5 = (4/3 + 3/4) · 5 = 16 + 9/12 · 5 = 125/12 = 105/12

б) $$\sqrt{3}$$; $$\sqrt{12}$$; ...
a₁ = $$\sqrt{3}$$
a₂ = $$\sqrt{12}$$
d = a₂ – a₁ = $$\sqrt{12}$$ – $$\sqrt{3}$$ = 2$$\sqrt{3}$$ – $$\sqrt{3}$$ = $$\sqrt{3}$$

S_n = $$\frac{2a_1 + d(n - 1)}{2}$$ · n

S₁₀ = $$\frac{2 · \sqrt{3} + \sqrt{3} · (10 - 1)}{2}$$ · 10 = (2$$\sqrt{3}$$ + 9$$\sqrt{3}$$) · 5 = 11$$\sqrt{3}$$ · 5 = 55$$\sqrt{3}$$