Решебник по алгебре 9 класс Мерзляк Задание 874

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$$1)c_4=216;q=-3:$$

$$c_4=c_1{q}^3$$

$$c_1=\frac{c_4}{q^3}=\frac{216}{(-3{)}^3}=-\frac{216}{27}=-8.$$

$$S_6=\frac{-8\cdot ((-3{)}^6-1)}{-3-1}=$$

$$=\frac{-8\cdot (729-1)}{-4}=2\cdot 728=$$

$$=1456.$$

$$2)c_1=5\sqrt{5};c_5=125\sqrt{5};$$

$$q>0$$

$$c_5=c_1{q}^4$$

$$q^4=\frac{c_5}{c_1}=\frac{125\sqrt{5}}{5\sqrt{5}}=$$

$$=25⟹q=\sqrt{5}.$$

$$S_6=\frac{5\sqrt{5}\cdot ({\left(\sqrt{5}\right)}^6-1)}{\sqrt{5}-1}=$$

$$=\frac{5\sqrt{5}\cdot (125-1)}{\sqrt{5}-1}=$$

$$=\frac{5\sqrt{5}\cdot 124\cdot (\sqrt{5}+1)}{(\sqrt{5}-1)(\sqrt{5}+1)}=$$

$$=\frac{620\sqrt{5}\cdot (\sqrt{5}+1)}{5-1}=$$

$$=155\cdot (5+\sqrt{5}).$$