soal barisan Geometri 1. diket: 4,2,1,1/2 .... dit: a. rumus b. U12 2. diket: U3=3 U5=27 dit: a.rumus b.U7 3. 3,-6,-12,-24.... 4. 1, 1/4 , 1/16 , 1/64....

1) Dik: 4, 2, 1 , 1/2, ...
• suku pertama = a = 4
• Rasio = 2
a) Rumus suku ke-n
Un = ar^n-1
= 4.2^n-1
= 2² . 2^n-1
= 2^n+1
b) Suku ke 12
Un = 2^n+1
U12 = 2^12+1
U12 = 2^13
U12 = 1024

2)
U3 = ar² = 3
U5 = ar⁴ = 27
• r² = 9
r = 3
•ar² = 3
a . 3² = 3
a . 9 = 3
a = 1/3
a) rumus suku ke-n
Un = ar^n-1
= 1/3 . 3^n-1
= 3^-1 . 3^n-1
= 3^n-2
b) suku ke 7
Un = 3^n-2
U7 = 3^7-2
U7 = 3^5
U7 = 729

3) -3,-6,-12,-24,-48
rasio = 2

4) 1, 1/4, 1/16, 1/64
a = 1
r = 1/4
a) Rumus suku ke n
Un = ar^n-1
= 1 . 1/4^n-1
= 1 . 4^1-n
= 4^n-1
b) Suku ke 7
Un = 4^n-1
U7 = 4^7-1
U7 = 4^6
U7 = 4096

5) 16,8,4,...,1/8
a = 16
r = 1/2
Un = 1/8
dit: Banyak suku(n)?
penyelesaian
Un = ar^n-1
1/8 = 16.1/2^n-1
2^-3 = 2⁴ . 2^-n+1
-3 = 4 + (-n + 1)
-3 = 4 - n + 1
-3 = 5 - n
5 - n = -3
n = 8