4) a1 = 3,6; d = 0,4; a(n) = 6,4
a(n) = a1 + d(n - 1)
6,4 = 3,6 + 0,4(n - 1) = 3,6 + 0,4n - 0,4 = 3,2 + 0,4n
0,4n = 6,4 - 3,2 = 3,2
n = 3,2/0,4 = 8
Это 8 член прогрессии.
6) 2x - 1 = b1; x + 3 = b2 = b1*q; x + 15 = b3 = b1*q^2
{ b1 = 2x - 1
{ b1*q = (2x - 1)*q = x + 3
{ b1*q^2 = (2x - 1)*q^2 = x + 15
Преобразуем
{ b1 = 2x - 1
{ q = (x + 3)/(2x - 1)
{ (2x - 1)*q*q = (x + 3)(x + 3)/(2x - 1) = x + 15
(x + 3)^2 = (2x - 1)(x + 15)
x^2 + 6x + 9 = 2x^2 + 29x - 15
0 = x^2 + 23x - 24 = 0
(x - 1)(x + 24) = 0
x1 = 1;
Прогрессия b1 = 1; q = (x+3)/(2x-1) = 4/1 = 4; b2 = x+3 = 4; b3 = x+15 = 16
x2 = -24;
Прогрессия b1 = -49; q = (x+3)/(2x-1) = 21/49 = 3/7;
b2 = x+3 = -21; b3 = x+15 = -9