Question

по заданному составьте геометрическую прогрессию - система: а2-a1=-4 и a3-a1=8 2)система :а1+а4=0,4375 и а3-а2+а1=0,875

Answer 1

1
{a2-a1=-4⇒a1q-a1=-4⇒a1(q-1)=-4⇒a1=-4/(q-1)
{a3-a1=8⇒a1q²-a1=8⇒a1=8/(q²-1)
-4/(a-1)=8/(q-1)(q+1)
-1=2/(q+1),q≠1
q+1=-2
q=-3
a1=-4/(-3-1)=-4/(-4)=1
an=1*(-3)^n-1=(-3)^n-1
2
{a1+a4=0,4375⇒a1+a1q³=0,4375⇒a1(1+q³)=0,4375⇒a1=0,4375/(1+q³)
{a3-a2+a1=0,875⇒a1q²-a1q+a1=0,875⇒a1(q²-q+1)=0,875⇒
a1=0,875/(q²-q+1)
0,4375/(1+q³)=0,875/(q²-q+1)
1/(1+q³)=2/(q²-q+1)
1/(q+1)(q²-q+1)=2/(q²-q+1)
1/(q+1)=2
q+1=0,5
q=-0,5
a1=0,4375/(1-0,125)=0,4375/0,875=0,5
an=0,5*(-0,5)^n-1