Question

Oblicz a1 i q.
a) a5=-1/2 , a10= -16
b) a4=24/100 a6= 96/125
c) a100=17 a253=17

Answer 1

A) a₅=-1/2 ; a₁₀=-16 ;
a₁₀=a₅×q⁵;
-16=-1/2×q⁵;
q⁵=-16/-1/2;
q⁵=32;
q=2;
a₅=a₁×q⁴;
-1/2=a₁×16/:16;
a₁=-1/32;
b)a₄=24/100 ; a₆=96/125;
a₆=a₄×q²;
96/125=24/100×q²;/:24/100;
q²=96/125:24/100;
q²=96/125×100/24;
q²=16/5;
q=4/√5=4√5/5;
a₄=a₁×q³;
24/100=a₁×(4√5/5)³;
a₁=24/100:64√5/25;
a₁=3/32√5=3√5/160;
c)a₁₀₀=17 ; a₂₅₃=17;
a₂₅₃=a₁₀₀×q¹⁵³;
17=17×q¹⁵³;
q¹⁵³=1;
q=1;
a₁×q⁹⁹=a₁₀₀;
a₁×1=17;
a₁=17;