Question

Tentukan hasil jumlah barisan bilangan ini yahh toling dibantu ya kak
a. 1,2,4,8,16,...(sampai 10 suku)
b. 54,18,6,2,...(sampai i9 suku)
c. 5,(-15),45,(-135),...(sampai 8 suku)
d. 1,1,3,2,9,4,27,8,...(sampai 19 suku)
e. 8,7,9,3,...,1/27,1/81=
tolong yahhh

Answer 1

A.    a = 1    dan r = 2
S10 = a(r^10 - 1) / (r -1) = 1 (2^10 - 1) / (2 - 1) = 2^10 - 1 = 1.024 - 1 = 1.023
b. a = 54 dan r = 1/3
S9 = a (1 - r^9) / (1 - r)
       = 54(1 - (1/3)^9) / (1 - 1/3)
     = 54 ( 1 - 1/19.683) / 2/3
     = 81 ( 19.682/19.683)
     = 19.682 / 243
   = 80,996

c. a1 = 5    dan r1 = 9
   a2 = -15  dan r2 = 9
S4 pertama = 5 (9^4 - 1) / (9-1) = 5 (6561 - 1) / 8 = 4100
S4 kedua = -15 (9^4 - 1) / (9-1) = -15(6561 - 1) / 8 = -12.300
S gabungan = 4.100 - 12.300 = - 8.200

d. a1 = 1    dan r1 = 3
a2 = 1 dan r2 = 2
S10 pertama = 1 (3^10 - 1) /(3 -1) = (59.049 - 1) / 2 = 29.524
S9 kedua = 1(2^10 - 1) /(2 - 1) = (1.024 - 1) / 1 = 1.023
s gabungan = 29.524 + 1.023 = 30.547