Kunci Jawaban Matematika Kelas 9 SMP Halaman 102, Latihan 2.3: Sumbu Simetri dan Titik Optimum

Soal nomor 4

Diketahui Un = an2 + bn + c
U1 = 1
U2 = 7
U3 = 16

Substitusi suku:
U1 = a(1)2 + b(1) + c
U1 = a + b + c
U2 = a(2)2 + b(2) + c
U2 = 4a + 2b + c
U3 = a(3)2 + b(3) + c
U3 = 9a + 3b + c

Sistem Eliminasi:
4a + 2b + c = 7
a + b + c = 1
3a + b = 6
6a + 2b = 12

9a + 3b + c = 16
a + b + c = 1
8a + 2b = 15

8a + 2b = 15
6a + 2b = 12
2a = 3
a = 3/2

Substitusi a = 3/2:
6 . 3/2 + 2b = 12
9 + 2b = 12
2b = 3
b = 3/2

a + b + c = 1
3/2 + 3/2 + c = 1
c = -2

Maka untuk mencari suku ke 100 adalah:
Un = an2 + bn + c
U100 = 3/2(100)2 + 3/2(100) + (-2)
U100 = 3/2. 10000 + 3/2. 100 – 2
U100 = 15000 + 150 – 2
U100 = 15148

Soal nomor 5

Diketahui Un = an2 + bn + c
U1 = 0
U2 = -9
U3 = -12
a(1)2 + b(1) + c = 0
a + b + c = 0
c = - a – b

Maka subtitusinya adalah
a(2)2 + b(2) + c = -9
4a + 2b + c = -9
4a + 2b + (-a-b) = -9
4a + 2b – a – b = -9
3a + b = -9

a(3)2 + b(3) + c = -12
9a + 3b + c = -12
9a + 3b + (-a – b) = -12
8a + 2b = -12
4a + b = -6

3a + b = -9
4a + b = -6
-a = -3
a = 3

3a + b = -9
3(3) + b = -9
b = -18