В арифметичній прогресії (хn): х4 + х2 – х3 = 4, х5 + х3 = 20 Знайти S9. *​

S9 = 144

Объяснение:

x4 = x1 + 3*d

x5 = x1 + 4*d

x2 = x1 + d

x3 = x1 + 2*d

х4 + х2 – х3 = 4 ,

x1 + 3*d + x1 + d - (x1 + 2*d) = 4

x1 + 2*d = 4

x1 = 4 - 2*d

х5 + х3 = 20

x1 + 4*d +x1+2*d = 20

2*x1 + 6*d = 20

x1 + 3*d = 10

4 - 2*d + 3*d = 10

4 + d = 10

d = 6

x1 = 4 - 2*d

x1 = 4 - 2*6

x1 = -8

S9 = (2*x1+8*d)/2*9

S9 = (-16 + 48)/2*9

S9 = 32/2*9

S9 = 144