1.
[tex]a_{8} = 1 = a_1\cdot q^{7}\\a_{5} = 27 = a_1\cdot q^{4}\\\\a_{8} = a_1\cdot q^{7} = 1\\a_5 = a_1\cdot q^{4} = 27\\\\\frac{a_8}{a_5} = q^{3} = \frac{1}{27}\\\\q^{3} = \frac{1}{27}\\\\\underline{q = \frac{1}{3}}\\\\a_1 = \frac{27}{q^{4}}=\frac{3^{3}}{(\frac{1}{3})^{4}} = 3^{3}\cdot3^{4} =3^{7}\\\\\underline{a_1 = 2187}\\\\a_{n} = a_1\cdot q^{n-1}\\\\\underline{a_{n} = 2187\cdot(\frac{1}{3})^{n-1}}[/tex]
2.
Z własności ciągu geometrycznego:
[tex]a_2^{2} = a_1\cdot a_3\\\\x^{2} = 48\cdot3\\\\x^{2} = 144\\\\x = \sqrt{144}\\\\\underline{x = 12}[/tex]
