Class: Add Maths - Chapter 1 Form 5 (Progressions) (part 1)
Salam kepada calon2 SPM semua. Bagaimana perasaan anda? Pasti nervous kan? Ok wat lek wat cool ok? Hehe ok hari ni saya nak ajar Add Maths form 5 bab 1 iaitu Progressions. Terbahagi kepada 2 iaitu
Arithmetic Progressions dan
Geometric Progression. First kita belajar Arimethic dulu ok?
ARITHMETIC PROGRESSIONS
Contoh satu rantai arithmetic progressions:
4, 7, 10, 13, 16...
Nilai '4' adalah sebutan pertama atau first term (T1). '7' adalah sebutan kedua atau second term (T2) dan selanjutnya. Perbezaan biasa atau common differencenya adalah 3 kerana setiap nilai dlm sebutan masing2 bila ditolak dgn nilai dalam sebutan sebelumnya adalah 3. Contoh '7-4=3 , 10-7=3 , 13-10=3, 16-13=3'. Ada faham?. Satu lagi contoh rantai progression:
3, 5, 8, 9, 11
Di atas ini BUKAN ARITHMETIC PROGRESSIONS kerana common differrence berbeza. Buktinya '5-3=2. 8-5=3, 9-8=1, 11-9=2'. Lihat kan? Sekejap 2, kejap 3, kejap 1. X konsisten so ianya bukan arithmetic progressions. Common differrence x semesti nombor genap seperi 2, 3, 4 dan sebagainya, ianya juga bole nombor pecahan, perpuluhan atau sebutan unknown (nombor yg tidak diketahui yg diganti dgn huruf.)
Formula untuk mencari nilai dalam sebutan ke berapa (nth term)
a= nilai first term (T1)
n=sebutan ke berapa
d=perbezaan biasa (common difference)
Formula untuk mencari jumlah dari nilai sebutan satu atau first term (T1) hingga ke sebutan n (n term)
Contoh soalan:
1) 2, 5, 8, 11...Find the common differrence
Jawapan: 3
Penyelesaian: 5-2=3 atau 8-5=3 atau 11-8=3
2) 4, 9, 14, 19...Find the 10th term of the arithmetic progressions.
Jawapan: 49
Penyelesaian: Gunakan formula nth term.
a=4
d=5
n=10
nth term=?
= 4 + (10-1)(5)
=49
3) 11, 14, 17, 20,........41. Find the number of term of 41.
Jawapan: 11
Penyelesaian: Gunakan formula nth term.
a=11
d=3
nth term=41
n=?
4) The fifth term of an arithmetic progressions is 13 and the 13th term is -19. Find the tenth term(10th)
Jawapan: -7
Ok kalau x faham sila komen ye? Ok next kita ke SUM OF ARITHMETIC pulak
Contoh:
1) 5, 1, -3, -7,.....Find the sum of first 8th term of arithmetic progressions
Jawapan: -72
Penyelesaian: Gunakan formula SUM OF nth TERM (Sn)
a=5
n=8
d=-4
S8=?
2) The forth term of A.P. is 3 and the sum of the first twelve termsis 96. Find the sum of all the terms from the sixth to twelve terms.
Jawapan: 91
Penyelesaian:
X paham tanye ok? Jgn buat2 faham...
Sekarang masa anda untuk buat latihan:
LATIHAN
1) 1.5, 2.7, 3,9,.....Find the nth terms of A.P. where n = 12
2) 31, 24, 17,....Find the number of term (n) where the the value of nth terms is -18.
3) The third term of an A.P. is 4 and the 8th terms is 49. Find
a) the first term (a) and the common differrence (d).
b) the 12th terms.
4) 1, 7/8, 3/4, ....Find the sum of first 10th of the A.P.
5) In an A.P. the first term (a) is 13 and the 15th terms is 111. Find
a) the common differrence (d)
b) the sum of first 10th terms.
6) In an A.P., the 4th terms is 3 and the sum of first 15th terms is -195. Find the sum of all the terms from the 10th terms to the 15th terms...
SELAMAT MENCUBA....KALAU X FAHAM ATAU BINGUNG SILA TINGGALKAN MESSENGE. SAMBUNGAN AKAN DIUPDATE KEMUDIAN
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