suatu barisan aritmatika diketahui U6 = 18 dan U10 = 30 jumlah suku 16 suku pertama dari barisan tersebut adalah.....

Diket:
u6 = 18
u10 = 30

Ditanya: s16?

Jawab:
Mencari nilai beda
[tex] \frac{30 - 18}{10 - 6} = \frac{12}{4} = 3[/tex]
Mencari nilai nilai a = u1
u6 = a + (6-1) × 3
18 = a + 5 × 3
18 = a + 15
a = 18 - 15
a = 3

Mencari nilai s16
[tex]sn = (2a + (n - 1)b) \frac{n}{2} \\ s15 = (2(3) + (15 - 1)3) \frac{15}{2} \\ s15 = (6 + (14)3) \times 7.5 \\ s15 = (6 + 42) \times 7.5 \\ s15 = 48 \times 7.5 \\ s15 = 360[/tex]

U10 = a + 9b
30 = a + 9b...(1
U6 = a + 5b
18 = a + 5b...(2

Eleminasi a pada pers. 1 dan 2
a + 9b = 30
a + 5b = 18 -
---------------------
4b = 12
b = 3
Subtitusi b = 3 ke pers. 2
a + 5b = 18
a + 5(3) = 18
a + 15 = 18
a = 18 - 15
a = 3

S16 = n/2 × (2a + b × (n-1))
= 16/2 × (2(3) + 3 × (16 - 1))
= 8 × (6 + 3 × (15))
= 8 × (6 + 45)
= 8 × 51
= 408