Question

1. Sa se gaseasca primii doi termeni ai progresiei geometrice (y indice n), data astfel:
a) y₁, y₂, 24, 36, 54, ...
b) y₁, y₂, 225, -135, 81, ...
2. Daca se cunosc doi termeni ai unei progresii geometrice (b indice n):
a) b₃ = 6, b₅ = 24, sa se gaseasca b₇, b₉, b₁₀
b) b₅ = 10, b₈ = -10, sa se gaseasca b₆, b₁₂, b₃

Answer 1

a)q=36/24=3/2
deci  32/3; 16, 24,36,...

b) q=-135/225=-27/45=-3/5⇒1/q=-5/3
y2= 225 *(-5/3)=-375
y1=-375* (-5/3)=625


2a) q²=24/6=4. q=2 sau q=-2

pt q=2 ca si pt q=-2, b7=b5 * q²=24*4=96;    b9=b7*q²=96*4=384
 b10=b9 *q=384*2=768 sau pt q=-2 sau  b10=-768


b) q³=-10/10=-1⇒q=-1
b6=b12=b8=-10
b3=b5=10