Perhatikan Soal UN SMA Tahun 2008 berikut ini. Tipe soal ini bisa ditemukan juga pada soal-soal UN SMA tahun sebelumnya.
Diketahui suku ke–3 dan suku ke–6 suatu deret aritmetika berturut–turut adalah 8 dan 17. Junlah delapan suku pertama deret tersebut sama dengan ….
A. 100
B. 110
C. 140
D. 160
E. 180
Tipe soal ini dikatakan BONUS karena trik penyelesainnya sederhana dan bisa lebih cepat. Penyelesaiannya akan lebih mudah bila kita memahami dengan baik cara menghitung Jumlah dari:
1 + 2 + 3 + 4 + …. + 99 + 100 (ini salah satu contoh Barisan Aritmatika)
Karena 1 + 100 = 2 + 99 = 3 + 98 = dst yaitu = 101
Kemudian karena ada 100 suku, maka Jumlahnya = ½.100.101 = 50.101 = 5.050
Kembali ke soal tadi, berarti ada 8 suku dari barisan bilangan aritmatika, atau bisa ditulis: U1 + U2 + U3 + U4 + U5 + U6 + U7 + U8
Karena barisan Aritmatika, maka pada kasus ini berlaku:
U1 + U8 = U2 + U7 = U3 + U6 = U4 + U5
Sehingga Jumlah 8 suku pertama = ½.8.(U3+U6) = 4.(8+17) = 4.25 = 100. (A)
Semoga bermanfaat.
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7 comments:
Makasi triknya. Ada lagi, nggak. Tak ikuti terus lo. Pasalnya, aku sekarang juga bantu ngajar di pondok pesantren Al-Multasam (SMA IPA).
Bisa kirim file-file soal try out atau semacamnya? Kirimkan ke: mulyoto@matematika.its.ac.id
Selamat Siang pak…
Salam Pendidikan dan Salam Kenal dari Balikpapan…
Boleh bertukar link..? :D
terimakasih pak penjelasannya sangat membantu sekali..
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