1) 4 - 3(n-1) > -60; 4 - 3n + 3 > -60; -3n > -67; n < -67/(-3) = 22 1/3
4 - 3n < -60; -3n < -64; n > 21 1/3
Ответ: n = 22
Проверка: a(21) = 4 - 3*21 = 4 - 63 = -59; a(22) = 4 - 3*22 = 4 - 66 = -62
2) a1 = -8; d = 3; Прогрессия: -8; -5; -2; 1; 4; 7
Ответ: 7
3) a1 = -3;
S(6) = (2a1 + 5d)*6/2 = 12; 2(-3) + 5d = 4; 5d = 4 + 6 = 10; d = 2
a3 = a1 + 2d = -3 + 2*2 = -3 + 4 = 1
Ответ: 1
4) b1 = 8; q = -1/2; Прогрессия: 8; -4; 2; -1
Ответ: -1
5) q = -4; S(3) = b1 + b1*q + b1*q^2 = b1 - 4b1 + 16b1 = 13b1 = 39
b1 = 39/13 = 3
S(5) = b1*(q^5 - 1) / (q - 1) = 3*(-4^5 - 1) / (-4 - 1) = 3*1025/5 = 615
Ответ: 615