U1=1 U2=3 U3=6 U4=10 U77?

Mapel : Matematika
Kelas : IX SMP
Bab : Barisan dan deret

Pembahasan :
1 , 3 , 6 , 10 , ...

Rumus Cepat...
2A = Konstanta
2A = [(U3 - U2) - (U2 - U1)]
2A = [(6 - 3) - (3 - 1)]
2A = [3 - 2]
2A = 1
A = 1/2

3A + B = Beda
3(1/2) + B = (U2 - U1)
3/2 + B = (3 - 1)
3/2 + B = 2
B = 2 - 3/2
B = 1/2

A + B + C = Suku Pertama
1/2 + 1/2 + C = 1
C = 0

Fungsi Kuadrat Kelas VIII
Un = An² + Bn + C
Un = 1/2n² + 1/2n
Un = 1/2n(n + 1)
U77 = 1/2(77)(78)
U77 = 3003

Bab Barisan dan Deret
Matematika SMP Kelas IX

1, 3, 6, 10.. → a = 1
   2, 3, 4,... → b = 2
      1, 1, ... → c = 1

Un = a + (n - 1) b + (1/2) x (n - 1) x (n - 2) x c
U77 = 1 + (77 - 1) x 2 + (1/2) x (77 - 1) x (77 - 2) x 1
U77 = 1 + (76 x 2) + (1/2) x 76 x 75
U77 = 1 + 152 + 2.850
U77 = 3.003