Question

Perhatikan barisan bilangan berikut 3,6,10,15,21 tentukan rumus suku ke-n dan jika Un = 136 tentukan nilai n yang memenuhi

Answer 1

3 , 6 , 10 , 15 , 21, ... => 3 = a + b + c
. +3 +4 .+5 .+6 =====> 3 = 3a + b
..... +1 .. +1 ..+1 ... =====> 1 = 2a
2a = 1 => a = 1/2
3a + b = 3 => 3(1/2) + b = 3 => b = 3 - 3/2 => b = 3/2
a + b + c = 0 => 1/2 + 3/2 + c = 3 => c = 1
Un = an^2 + bn + c
Un = 1/2 n^2 + 3/2 n + 1
Un = 1/2 (n^2 + 3n + 2)
Un = 1/2 (n + 2)(n + 1)

Un = 136
1/2 n^2 + 3/2 n + 1 = 136
n^2 + 3n + 2 = 272
n^2 + 3n - 270 = 0
(n + 18)(n - 15) = 0
n = -18 atau n = 15
Ambil yg positif : n = 15