Question

Найдите сумму первых 15 членов арифметической прогрессии {an}:

1) a5=27, a27=60;
2)a20=0, a66=-92;
3)a1=-3, a61=57;
4)a1=-10,5, a63=51,5.

Answer 1

1. \left \{ {{ a_{5} = a_{1}+4d } \atop { a_{27} = a_{1}+26d }} ⇒ \left \{ {{27= a_{1} +4d} \atop 60= a_{1}+26d }} \right. ⇒ a_{1} = 21; d = 1.5; S_{n} = 2(21+1.5*7)/2 = 31.5;
2.  \left \{ {{ a_{20} = a_{1}+19d } \atop { a_{66} = a_{1}+ 65d}} ⇒ a_{1} = -38; d= -2; S_{15} = \frac{2*38+2*14}{2} = 24; 
3.\left \{ {{ a_{61} = a_{1} +60d} \atop { a_{1} =-3}} \right. ⇒ d=1  S_{15} = \frac{2*(-3)+14}{2} = 4;
4.d=1;  $S_{15} = \frac{2*(-10.5+14)}{2} = -3.5$