Dari suatu barisan aritmetika, suku ketiga adalah 36, jumlah suku kelima dan ketujuh adalah 144. Suku kesepuluh barisan tersebut adl... A. 112 B. 116 C. 118 D.

Materi Barisan dan Deret

[tex] \text{Diketahui} \\ u_3 = a + 2b = 36 \\ u_5 + u_7 = a + 4b + a + 6b \\ = 2a + 10b = 144 \Rightarrow a + 5b = 72 [/tex]
Lakukan metode penyelesaian SPLDV
a + 2b = 36
a + 5b = 72
---------------- -
-3b = -36
b = 12 => a + 24 = 36 => a = 12
[tex] u_{10} = a + 9b = 12 + 9(12) = 120 [/tex]
Jawaban D

U3 = 36
U5 + U7 = 144
U10 = ...?
Jawab :
U3 => a + 2b = 36 ····· (1)
U5 + U7
=> a + 4b + a + 6b = 144
=> 2a + 10b = 144 ····· (2)

a + 2b = 36 | x2 |
2a + 10b = 144 | x1 |
_______________
2a + 4b = 72
2a + 10b = 144
____________ --
........ -6b = -72
............ b = -72/-6 = 12

a + 2b = 36 ····· (1)
a + 2 (12) = 36
a + 24 = 36
a = 36 - 24 = 12

Maka,
U10 = a + 9b
U10 = 12 + 9 ( 12 )
U10 = 12 + 108
U10 = 120
Jawaban : D