MODUL • MATEMATIK TAMBAHAN TINGKATAN 5 2 © Nilam Publication Sdn. Bhd. (919810-T) U N I T 1 2 Nyatakan beza sepunya bagi setiap janjang aritmetik yang berikut. State the common difference of each of the following arithmetic progressions. d = –45 – (–52) = 7 (a) 15, 7, –1, ... (c) 1 3 , 7 12 , 5 6 , 13 12 , ... (b) 20.8, 18.3, 15.8, ... (d) –16, –10, –4, ... (e) 65, 66 1 2 , 68, ... –52, –45, –38, … Penyelesaian: Solution: Jawapan: Answer: Jawapan: Answer: Jawapan: Answer: Jawapan: Answer: Jawapan: Answer: Sebutan ke-n bagi suatu janjang aritmetik diberi oleh / The n th term of an arithmetic progressions is given by T n = a + ( n – 1) d Sebutan pertama / First term Bilangan sebutan / Number of term Beza sepunya / Common difference Jawapan: Answer: Jawapan: Answer: Jawapan: Answer: Jawapan: Answer: (c) 11.6, 11.2, 10.8, … (e) y , 8 y , 15 y , … (b) 1 2 , – 3 4 , 1, – 5 4 , ... (d) p , p + 4, p + 6, ... Contoh / Example d = – 3 4 – 1 2 = – 5 4 d = 1 – – 3 4 = 7 4 d = – 5 4 – 1 = – 9 4 tiada beza sepunya, ∴ bukan janjang aritmetik no common diiference, ∴ not arithmetic progression d = 11.2 – 11.6 = –0.4 d = 10.8 – 11.2 = –0.4 ∴ d = –0.4, Janjang aritmetik Arithmetic progression T 2 – T 1 = p + 4 – p = 4 T 3 – T 2 = ( p + 6) – ( p + 4) = 2 ∴ tiada beza sepunya, ∴ bukan janjang aritmetik common diiference, ∴ not arithmetic progression T 2 – T 1 = 8 y – y = 7 y T 3 – T 2 = 15 y – 8 y = 7 y ∴ d = 7 y , Janjang aritmetik Arithmetic progression d = 7 – 15 = –8 d = 7 12 – 1 3 = 1 4 d = –10 – (–16) = 6 d = 18.3 – 20.8 = –2.5 d = 66 1 2 – 65 = 1 1 2 MMP Add Math Tg5 C1.indd 26/9/2013 12:12:56 PM