jumlah bilangan bulat antara 1 sampai 2015 yang kelipatan 6 dan tidak kelipatan 5 ????

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

Pembahasan :
kelipatan 6...
6, 12 , 18 ,... , 2010

Un = 2010
a + (n - 1)b = 2010
6 + 6n - 6 = 2010
6n = 2010
n = 335

Sn = n/2(a + Un)
S335 = 335/2(6 + 2010)
S335 = 335/2(2016)
S335 = 335(1008)
S335 = 337.680

Bilangan kelipatan 6 dan 5 (kelipatan 30)
30 , 60 , 90 , ... , 2010

Un = a + (n - 1)b
2010 = 30 + (n - 1)30
2010 = 30 + 30n - 30
2010 = 30n
n = 2010/30 = 67

Sn = n/2 (a + Un)
S67 = 67/2 (30 + 2010)
S67 = 67/2 × 2040
S67 = 68.340

Bilangan yg kelipatan 6 , tapi tdk kelipatan 5
= 337.680 - 68.340
= 269.340

Bil antara 1 - 2015

Kelipatan 6
6 , 12 , 18 , .... , 2010

a = 6
b = 6
Un = a + (n - 1)b
2010 = 6 + (n - 1)6
2010 = 6 + 6n - 6
2010 = 6n
n = 2010/6 = 335

Sn = n/2 (a + Un)
S335 = 335/2 (2010 + 6)
S335 = 337.680

Bilangan kelipatan 6 dan 5 --> kelipatan 30

30 , 60 , 90 , ... , 2010
a = 30
b = 30
Un = a + (n - 1)b
2010 = 30 + (n - 1)30
2010 = 30 + 30n - 30
2010 = 30n
n = 2010/30 = 67

Sn = n/2 (a + Un)
S67 = 67/2 ( 30 + 2010)
S67 = 67/2 × 2040
S67 = 68.340

Bilangan yg kelipatan 6 , tetapi tdk kelipatan 5
= 337.680 - 68.340
= 269.340