1. Найдите семнадцатый член арифметической прогрессии (An), если а=-17, а d=5.2.

1) a(1) = -17, d = 5,2. a(17) = ?.

a(n) = a(1) + (n - 1)d = -17 + (n - 1) * 5,2 = -17 + 5,2n - 5,2 = 5,2n - 23,2;

a(17) = 5,2 * 17 - 23,2 = 65,2.

2) a(1) = 37, a(2) = 33, a(3) = 29. S(20) = ?.

d = a(2) - a(1) = 33 - 37 = -4;

a(n) = a(1) + (n - 1)d = 37 + (n - 1) * (-4) = 37 - 4n + 4 = -4n + 41;

S(n) = (a(1) + a(n)) / 2 * n = (37 - 4n + 41) / 2 * n = (39 - 2n)n;

S(20) = (39 - 2 * 20) * 20 = -1 * 20 = -20.

3) a(n) = 3n - 4. S(40) = ?.

S(40) = (-1 + 3 * 40 - 4) / 2 * 40 = 2300.