Question

Dane: a1=-4, q=1/5, Sn=1/5. Wyznacz n i an ciągu geometrycznego.

Answer 1

A1=-4, q=1/5, Sn=1/5

Sn= a₁*[1-q(don)/1-q]

1/5 = -4*[ 1-(1/5)(don)/1-1/5]

1/5 = -4*[(1-(1/5)(don)/(-4/5)]/:(-4)

-1/20=[(1-(1/5)(don)*(-5/4)]/:(-5/4)

1/25=[1-(1/5)(don)]

1/25-1=-(1/5)(don)

-24/25=-(1/5)(don)/*(-1)

24/25=1/5(don)

24*(1/5)²-(1/5)(don)=0

podstawmy za (1/5)(don)=t


t= 24/25

zatem 24/25=(1/5)(don)

n =2
an=a₁*q(do n-1)

an=-4*(1/5)=-4/5