1.
[tex]a_5 = 11 = a_1 + 4n\\a_{15} = 15 = a_1 + 14r\\\\a_1+14r = 15\\a_1 +4r = 11\\------- \ \ \ odejmujemy \ stronami\\10r = 4 \ \ /:10\\\underline{r = 0,4}\\\\a_1 = 11-4r = 11-4\cdot0,4 = 11-1,6\\\underline{a_1 = 9,4}\\\\S_{n} = \frac{2a_1+(n-1)\cdot r}{2}\cdot n\\\\S_{16} = \frac{2\cdot9,4+15\cdot0,4}{2}\cdot 16\\\\S_{16} = \frac{18,8+6}{2}\cdot16\\\\S_{16} = 24,8\cdot8\\\\\boxed{S_{16} = 198,4}[/tex]
2.
[tex]a_1 = 5\\a_2 = 10\\r = a_2-a_1 = 10-5\\\underline{r = 5}\\\underline{a_{n} = 295}\\\\a_{n} = a_1 + (n-1)\cdot r\\\\295 = 5 + (n-1)\cdot5\\\\295 = 5 + 5n-5\\\\295 = 5n \ \ /:5\\\\\underline{n = 59}\\\\\\S_{n} = \frac{2a_1+(n-1)}{2}\cdot r\\\\S_{59} = \frac{2\cdot5+58\cdot5}{2}\cdot59\\\\S_{59} = \frac{10+290}{2}\cdot59\\\\S_{59} = 150\cdot59\\\\\boxed{S_{59} = 8 \ 850}[/tex]
