Question

80 баллов, арифметические прогрессии

Answer 1

$\displaystyle\tt 1.\\\\ a_1+2d=a_3\\2\sqrt{5}-11+2d=2-3\sqrt{5} \\2d=2-3\sqrt{5}- 2\sqrt{5}+11\\ 2d=13-5\sqrt{5} \\\\ a_5=a_3+2d=2-3\sqrt{5}+13-5\sqrt{5}=\bold{15-8\sqrt{5}}$

$\displaystyle\tt 2.\\\\a_n=4n-3\\a_1=4\cdot1-3=1\\a_{26}=4\cdot26-3=101\\\\ S_{26}=\frac{a_1+a_{26}}{2}\cdot 26= (a_1+a_{26})\cdot13=(1+101)\cdot13=\bold{1326}$