Question

Для прогрессии {un} выполнены равенства u1 +u5=51 и u2+u6=102. при каком значении n верно равенство sn=3069

Answer 1

$u_1 + u_5 = 51\\\\ u_2 + u_6 = 102\\\\ u_2 = u_1*d, \ u_6 = u_5*d\\\\ d*(u_1 + u_5) = 102\\\\ d = 2\\\\ u_5 = u_1*d^4\\\\ u_1 + u_1*d^4 = 51\\\\ u_1 = \frac{51}{1 + 16} = 3\\\\ S_n = u_1*\frac{d^n -1}{d - 1} = 3069\\\\ 3*2^n - 3 = 3069\\\\ 3*2^n = 3072\\\\ 2^n = 1024\\\\ \boxed{n = 10}$