Question

Determinati in fiecare caz x E lR, stiind ca urmatoarele numere sunt termeni conse-

cutivi ai unei progresii aritmetice:

a) x, (x _1)2 , X + 2 ; b) x, 2x-5, x-4;

c) x-I, x + 1, 2x -1 ;


d) x+1, 1-x,4.

Answer 1

Daca a,b si c sunt termenii consecutivi ai unei p.g atunci b = (a+c)/2

a) x, (x-1)2, x+2

(x-1)2 = (x+x+2)/2

x-1 = 2x+2

x-2x = 2+1

-x = 3

x = -3

b) 2x-5= (x+x-4)/2

4x-10 = 2x-4

4x-2x = -4+10

2x = 6

x = 3

c) x+1 = (x-1+2x-1)/2

2x+2 = 3x-2

2x-3x = -2-2

-x = -4

x = 4

d) 1-x = (x+1+4)/2

2-2x = x+5

-2x -x = 5-2

-3x = 3

x = -1