Suatu deret arimatika mempunyai suku ke -5 bernilai 30 dan suku ke -12 bernilai 16. jumlah tiga puluh suku pertama deret tersebut adalah

Jawabannya:

Mapel. : Matematika
Bab. : Barisan dan Deret Aritmatika
Sub Bab : Deret Aritmatika

Pembahasan:

U12 → a + 11b = 16
U5 → a + 4b = 30
--------------------------- -
7b = -14
b = -14/7
b = -2

Maka:
a + 4b = 30
a = 30 - 4b
a = 30 - 2(-2)
a = 30 - (-4)
a = 34

Maka :

Jumlah 30 suku pertama :

Sn = n/2. (2a + (n - 1). b)
S30 = 30/2. (2. 34 + (30 - 1). -2
S30 = 15. (68 + (29. (-2))
S30 = 15. (68 + (-58))
S30 = 15. (10)
S30 = 150 → Jwbnya

# Maaf Kalo Salah

Un = a + (n-1) b
U5 = a + (5-1) b
30 = a +4b

U12= a + (12-1)b
16 = a + 11b

=> a + 4b = 30
a + 11b = 16
___________ _
-7b = -14
b = -14/-7
b = 2

=> a + 4b = 30
a + 4x2 = 30
a + 8 =30
a = 30 -8
a = 22

U30 = a + 29 x b
= 22 + 29 x 2
= 22 + 58
= 80

S30 = n/2 (a+U30)
= 30/2 (22 + 80)
= 15 x 102
= 1.530