Question

Tentukan banyak suku dari barisan 1 1. 6+9+12+15+....=756
2. 56+51+46+41+...=-36
3. 10+14+18+22+...=640

Answer 1

1) 6 + 9 + ... + ... = 756
a = 6
b = 9
Un = a + (n - 1)b
     = 6 + 9(n - 1)
     = 9n - 3
Sn = (n/2)(a + Un)
756 = (n/2)(6 + 9n - 3)
756 = (9n² + 3n)
9n² + 3n - 756 = 0
n = 9

2) 56 + 51 + 46 + 41 + ... = - 36
a = 56
b = 51 - 56 = - 5
Un = 56 - 5(n - 1)
     = - 5n + 61
Sn = (n/2)(a + Un)
- 36 = (n/2)(56 - 5n + 61)
- 36 = (-5n² + 117n)
5n² - 117n - 36 = 0

Answer 2

1). a=6, b=3, Sn=756
Sn=n/2(2a+(n-1)b)
756=n/2(2.6+(n-1)3)
756=n/2(12+3n-3)
756=n/2(3n+9)
1512=3n²+9n ---> dibagi 3
n²+3n-504=0
(n+24)(n-21)=0
n=21

2). a=56, b=-5, Sn=-36
Sn=n/2(2a+(n-1)b)
-36=n/2(2.56+(n-1)-5)
-36=n/2(112-5n+5)
-36=n/2(117-5n)
-72=-5n²+117n
5n²-117n-72=0
(5n+3)(n-24)=0
n=24

3). a=10, b=4, Sn=640
Sn=n/2(2a+(n-1)b)
640=n/2(2.10+(n-1)4)
640=n/2(20+4n-4)
640=n/2(4n+16)
640=n(2n+8)
2n²+8n-640=0
n²+4n-320=0
(n+20)(n-16)=0
n=16