Найдите первый член и разность арифметической прогрессии{сn}, если: 1) с5=27, с27=60.2) с20=0, с66=-92.

c (n) = c (1) + (n - 1) d.

1) c (5) = c (1) + 4d = 27,

c (27) = c (1) + 26d = 60;

26d - 4d = 60 - 27;

22d = 33;

d = 33 / 22 = 3/2;

c (1) = 27 - 4 · 3/2 = 27 - 6 = 21.

2) c (20) = c (1) + 19d = 0,

c (66) = c (1) + 65d = - 92;

65d - 19d = - 92 - 0;

46d = - 92;

d = - 92 / 46 = - 2;

c (1) = 0 - 19 · (-2) = 38.