Penjelasan dengan langkah-langkah:
diketahui:
u5 = 11
u8 + u12 = 52
dit : u15..?
penyelesaian:
a +(n - 1)b = un
a + (5 - 1) b = u5
a + 4b = 11 ......(1)
a +(n - 1)b = un
(a +(n - 1)b ) + (a +(n - 1)b ) = u8 + u12
[ a + (8 - 1)b ] + [ a +(12 - 1)b ] = 52
a + 7b + a + 11b = 52
2a + 18b = 52 .... (2)
▪ Eliminasi a pada persamaan (1) dan (2)
a + 4b = 11 | × 2 | 2a + 8b = 22
2a + 18b = 52 | × 1 | 2a + 18b = 52 (-)
- 10b = - 30
b = 3
▪ substitusi b ke persamaan (1)
a + 4b = 11
a + 4( 3 ) = 11
a + 12 = 11
a = 11 - 12
a = - 1
▪ jumlah 15 suku pertama deret tersebut :
[tex]sn = \frac{n}{2}( 2a + (n - 1)b \\ \\ s15 = \frac{15}{2} (2( - 1) + (15 - 1)3 \\ \\ s15 = \frac{15}{2} ( - 2 + (14 \times 3) \\ \\ s15 = \frac{15}{2} ( - 2 + 42) \\ \\ s1 5= \frac{15}{2} \times 40 \\ \\ s15 = 300[/tex]
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