Question

Barisan Geometri diketahui Jumlah sampai suku ke 4 (S4) = 105,
dan jumlah sampai suku ke delapan(S8) = 1.785
tentukan suku pertama dan rasionya ....
(tolong ya..)

Answer 1

S4 = a(r^4-1) / (r-1) = 105
S8 = a(r^8-1) /(r-1) = 1.785

S8/S4--> a(r^8-1) / (r-1) : a(r^4-1) /(r-1) = 1.785/105

(r^8-1) : (r^4-1) = 17
(r^4-1) (r^4+1) : (r^4-1) = 17
r^4 +1 = 17
r^4 = 16
r^2 =√16=4
r = √4 = 2

 a(r^4-1) / (r-1) = 105
a(2^4-1) /( 2-1) = 105

a(16-1) /1= 105
a(15) = 105
a= 105/15
a= 21