diketahui u3=27 , u5=3 , tentukan : A. suku ke 6 , B. jumlah 6 suku pertama

dik : U3 = 27 ; U5 = 3
dit: a) U6
b) S6

jawab:
U3 = ar² = 27
U5 = ar^4 = 3

U5 = ar².r² = 3
27 . r² = 3
r² = 3/27 >> r² = 1/9
r = √1/9 = 1/3
untuk cari a, substitusikan aja
27 = a.r²
27 = a.(1/3)²
27 = a.1/9 >> a = 27 × 9 = 243

a) Un = ar^n-1
U6= 243.(1/3)^5
U6= 243.1/243 = 1

U5 = 3
ar^4 = 3
ar^2.r^2 = 3
27. r^2 = 3
r^2 = 3/27
r^2 = 1/9
r = 1/3

U3 = a.r^2
27 = a.1/9
a = 243

A.
U6
= a.r^5
= (243) (1/3)^5
= (243) (1/243)
= 1

B.
S6
= a ( r^n - 1 ) ÷ r - 1
= 243 ( (1/3)^6 - 1 ) ÷ ( 1/3 ) - 1
= 243 ( 1/729 - 1 ) ÷ ( -2/3)
= 243 ( -728/729 ) ÷ ( -2/3 )
= 364