Question

Diketahui Deret Geometri dengan S2=72 dan S4=80. Hitung Nilai U5

Answer 1

Deret Geometri

S2=72
S4=80

U5?

Sn=a(r^n-1)/(r-1)
S2=a(r^n-1)/(r-1)
72=a(r^n-1)/(r-1)
72(r-1)=a(r^2-1)
72(r-1)/(r^2-1)=a

S4=a(r^n-1)/(r-1)
80=a(r^4-1)/(r-1)
80(r-1)=a(r^4-1)
80(r-1)/(r^4-1)=a

72(r-1)/(r^2-1)=80(r-1)/(r^4-1)
72(r-1)(r^4-1)=80(r-1)(r^2-1)
72(r^5-r^4-r+1)=80(r^3-r^2-r+1)
72r^5-72r^4-72r+72=80r^3-80r^2-80r+80
72r^5-72r^4-80r^3+80r^2-72r+80r+72-80=0
Faktorkan:
72r^5-72r^4-80r^3+80r^2+8r-8=0

metode Horner
72. -72 -80. 80 8. -8
1/3. 24 -16 -32 16. 8
----------------------------- (+)
72 -48 -96. 48 24. 0

(r-1/3)(72r^4-48r^3-96r^2+48r+24)

r=1/3

a=72(1-r)/(1-r^2)
a=72(1-1/3)/(1-1/3^2)
a=72(3/3-1/3)/(9/9-1/9)
a=72(2/3)/(8/9)
a=48/(8/9)
a=48x(9/8)
a=54

U5=ar^4
=54.1/3^4
=54.1/81
=54/81
=6/9
=2/3
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Demikian semoga membantu dan bermanfaat!