Răspuns:
Explicație pas cu pas:
a) [tex]b_{2}[/tex]=6*2=12
[tex]b_{3}[/tex]=6*[tex]2^{2}[/tex] =24
[tex]b_{4}[/tex]=[tex]b_{3}[/tex]*q=24*2=48
[tex]b_{5}[/tex]=[tex]b_{4}[/tex] *q
b) [tex]b_{2}[/tex]=[tex]b_{1}[/tex] *q
-10=[tex]b_{1}[/tex] * [tex]\frac{1}{2}[/tex]
[tex]b_{1}[/tex]=-20
[tex]b_{3}[/tex]=[tex]b_{2}[/tex] *q=-[tex]\frac{10}{2}[/tex]=-5
[tex]b_{4}[/tex]=[tex]b_{3}[/tex] *q=[tex]\frac{-5}{2}[/tex]
[tex]b_{5}[/tex]=[tex]b_{4}[/tex] *q=[tex]\frac{-5}{4}[/tex]
2. a) [tex]b_{1}[/tex]=5
[tex]b_{2}[/tex]=25
[tex]b_{2}[/tex]=[tex]b_{1}[/tex]*q => q=25:5=5
x=[tex]b_{3}[/tex]=25*5=125
y=[tex]b_{4}[/tex]=125*5=625
z=625*5=3125
b) [tex]b_{4}[/tex]=[tex]b_{3}[/tex]*q => 36=24q =>q=36:24=[tex]\frac{3}{2}[/tex]
[tex]b_{3}[/tex]=[tex]b_{2}[/tex]*q
24=y * [tex]\frac{3}{2}[/tex] => y=48:3=16
[tex]b_{2}[/tex]=[tex]b_{1}[/tex]*q
16=x*[tex]\frac{3}{2}[/tex] => x=[tex]\frac{32}{3}[/tex]
c) 9=1* [tex]q^{2}[/tex] => q=+/- 3
z=3 sau z=-3
y=9*3=27 sau y=-27
z=81*3=163 sau z=-163
3) a) b3=b1 * q^2
b5=b1* q^4
b5 : b3= q^2 => q^2=24:6=4 => q=2
b1=b3 : q^2=6/4=3/2
b)[tex]\left \{ {{b1 *q-b1=4} \atop {b1* q^2 -b1=-8
}} \right.[/tex] => [tex]\left \{ {{b1(q-1)=4} \atop {b1(q -1)(q+1)=-8
}} \right.[/tex] => q+1=-8:4=-2, b1=4: (-3)=-4/3
c) [tex]\left \{ {{b1(1+q+q^2)=7} \atop {b1*q(1+q+q^2)=14}} \right.[/tex]
prima împărțită la a doua => q=14/7=2
b1(1+2+4)=7 => b1=7/7=1
