Tentukan hasil dari ( tanpa menghitung satu per satu) A. 2+4+6+8+10+...+100 B. -1+2-3+4-5+6-7+8-...+100 C. -100-99-98-...-2-1-0+1+2+...+97+98+99

Penyelesaian:

A. 2 + 4 + 6 + 8 + ... + 100
a = 2 
b = 2

Un = a + (n-1)b
100 = 2 + (n-1)2
n = 50

Sn = n/2 (2a + (n-1)b)
= 50/2 (2(2) + (50-1)2)
= 25 (102)
Sn = 2,550

B. -1 + 2 - 3 + 4 - 5 + 6 - 7 + ... + 100
dapat dipecah menjadi 2 barisan bilangan:
barisan bilangan 1 = -1 - 3 - 5 - 7 - ... - 99
a = -1 ; b = -2

Un1 = a + (n-1)b
-99 = -1 + (n-1)(-2)
n = 50

Sn = n/2 (2a + (n-1)b)
= 50/2 (2(-1) + (50-1)(-2)
= 25 (-100)
Sn1 = -2,500

barisan bilangan 2: 2 + 4 + 6 + 8 + ... + 100
a = 2 ; b = 2

Un = a + (n-1)b
100 = 2 + (n-1)2
Un2 = 50

Sn2 = 50/2 (2(2) + (50-1)(2)
= 25 (4 + 98)
= 25 (102)
Sn2 = 2,550 

Sn2 - Sn1 = 2,550 - 2,500 = 50

C. -100 - 99 - 98 - ... + 99
a = -100 ; b = 1

Un = a + (n-1)b
99 = -100 + (n-1)(1)
n = 200

Sn = n/2 (2a + (n-1)b)
= 200/2 (2(-100) + (200-1)(1)
= 100 (-200 + 199)
= 100 (-1)
Sn = -100