Question

Barisan aritmatika suku ke-7 : 22 suku ke 11 :34. jumlah 18 suku pertama adl

Answer 1

22 = a +  6b
34 = a + 10b  -
-12 = -4b
12 = 4b
12 : 4 = b
3 = b

cari suku awal
22 = a + 6b
22 = a + (6 x 3)
22 = a + 18
a = 22-18
a = 4

sehingga a = 4, b = 3

Sn = n/2 (2a + (n-1)b)
S18 = 18/2 [(2 x 4) + (18-1)3]
S18 = 9 [8 + (17 x 3)]
S18 = 9 (8 + 51)
S18 = 9 (59)
S18 = 531

Answer 2

Un=a+(n-1)b
U7= 22 ⇒   a+(7-1)b =22 ⇔a+6b=22.....(1)
U11=34 ⇒   a+(11-1)b =34 ⇔ a+10b=34.....(2)
eliminasi persamaan 1 dan 2:
 a +  6b =22
 a + 10b =34 -
-4b = -12
b = -12/-4 =3

subs. b:
a + 6b =22
a +6(3) = 22
a = 22-18
a= 4

jadi, a = 4, b = 3

Sn = n/2 (2a + (n-1)b)
S18 = 18/2 [(2 x 4) + (18-1)3]
S18 = 9 [8 + (17 x 3)]
S18 = 9 (8 + 51)
S18 = 9 (59)
S18 = 531
jadi, S18= 531