7.
[tex]a_1 =2\\q = \frac{1}{2}\\n = 10\\S_{10} = ?[/tex]
[tex]S_{n} = a_1\cdot\frac{1-q^{n}}{1-q}\\\\S_{10} = 2\cdot\frac{1-(\frac{1}{2})^{10}}{1-\frac{1}{2}} = 2\cdot\frac{1-\frac{1}{1024}}{\frac{1}{2}} = 2\cdot\frac{\frac{1024}{1024}-\frac{1}{1024}}{\frac{1}{2}} =2\cdot\frac{1023}{1024}\cdot2 = 4\cdot\frac{1023}{1024} = \frac{1023}{256}[/tex]
8.
[tex]a_1 = 4\\a_3 = 16\\a_2 = ?[/tex]
Z własności ciągu geometrycznego:
[tex]a_2^{2} = a_1\cdot a_3\\\\a_2^{2} = 4\cdot16\\\\a_2^{2} = 64\\\\a_2 = 8, \ \ (ciag \ jest \ rosnacy)[/tex]
