tentukan hasil dari(tanpa menghitung satu persatu) A. 1+3+5+7+9+...+99 B. 1-2+3-4+5-6+7-8+...-10 C. –100-99-98-...-2-1-0+1+2+...+48+49+50

A.
A = 1
B = 3-1 = 2

Banyak suku :
= 99/2
= 49,5 (50)

S50 :
= n/2 x (a + Un)
= 50/2 x (1 + 99)
= 25 x 100
= 2500

B.
1-2 = -1
3-4 = -1
.. - .. = -1
9-10 = -1

Banyak kali penjumlahan :
= 10 :2
= 5

Maka hasilnya :
= -1 x 5
= -5

C.
A = -100
B = -99 - (-100) = 1

Banyak suku :
= 100 + 1 + 50
= 151

S151 :
= n/2 (a + Un)
= 151/2 (-100 + 50)
= 75,5 x (-50)
= -3775

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

Pembahasan :
Un = 2n - 1
99 = 2n - 1
2n = 100
n = 50

1 + 3 + 5 + 7 + ... + 99 = n²
1 + 3 + 5 + 7 + ... + 99 = 50²
1 + 3 + 5 + 7 + ... + 99 = 2500

————————————————
1 - 2 + 3 - 4 + ... - 10
= -1 - 1 - 1 - 1 - ... - 1
= -(1 + 1 + ... + 1)
= -(10/2)
= -5

————————————————
Un = 50
a + (n - 1)b = 50
-100 + n - 1 = 50
n - 101 = 50
n = 151

-100 - 99 - 98 - ... + 50
= S151
= 151/2(-100 + 50)
= 151/2(-50)
= -3775