Question

15 Wyznacz takie liczby: x, y, z, aby ciąg był arytmetyczny. a) 4, x, y, z, 11 b) x, 4, y, 11, z​

Answer 1

ciag artmetyczny to taki w ktorym kazda kolejna liczba rosnie(lub maleje) dokladnie o r (roznice)

a) 4, x, y, z, 11

a1 = 4

x  = a1 + r                 = 4 + r

y = x + r = 4+r + r     = 4 + 2r

z = y + r = 4+2r+r     = 4+3r

11 = z + r = 4 + 3r + r = 4 + 4r

11= 4 + 4r

7 = 4r

r = 7/4

x = 4 + r = 16/4 + 7/4 = 23/4

y = 4 + 2r = 16/4 + 14/4 = 30/4

z = 4 + 3r = 16/4 + 21/4 + 37/4

b) x, 4, y, 11, z

x = a2 - r   = 4 -r

a2 = 4

y = a2 + r = 4 + r

11 = y + r = 4 +2r

z = 11 + r

11 = 4 +2r

7 = 2r

r = 3.5

x = 4-r = 0.5

y = 4+r = 7.5

z = 11+ 3.5 = 14.5