Jika diketahui barisan aritmetika dengan suku ke−3=−4 1/2 dan suku ke−8=−2. Tentukan suku pertama, beda, serta Tahap penyelesaian rumus suku ke−n dari barisan tersebut.

<p>Jawaban : a = -5 1/2 , b = 1/2 dan Un = -6 + n/2&nbsp;</p><p>&nbsp;</p><p>Konsep :&nbsp;</p><p>Rumus suku ke-n Un = a + (n-1)b&nbsp;</p><p>Keterangan&nbsp;</p><p>Un = suku ke-n&nbsp;</p><p>a = suku pertama&nbsp;</p><p>b = beda&nbsp;</p><p>&nbsp;</p><p>Pecahan Campuran&nbsp;</p><p>A B/C = ((C . A) + B)/C&nbsp;</p><p>Pembagian Pecahan&nbsp;</p><p>A/B : C = A/B x 1/C&nbsp;</p><p>&nbsp;</p><p>Pembahasan :&nbsp;</p><p>U3 = -4 1/2&nbsp;</p><p>a + (3-1)b = -4 1/2&nbsp;</p><p>a + 2b = -4 1/2 . . .(i)&nbsp;</p><p>&nbsp;</p><p>U8 = -2&nbsp;</p><p>a + (8-1)b = -2&nbsp;</p><p>a + 7b = -2 . . .(ii)&nbsp;</p><p>&nbsp;</p><p>Eliminasikan (i) dan (ii)&nbsp;</p><p>a + 2b = -4&nbsp;</p><p>1/2 a + 7b = -2&nbsp;</p><p>----------------------- -&nbsp;</p><p>-5b = -2 1/2&nbsp;</p><p>b = (-2 1/2)/-5&nbsp;</p><p>b = (2 1/2)/5&nbsp;</p><p>b = (((2 . 2)+1)/2) : 5&nbsp;</p><p>b = 5/2 x 1/5&nbsp;</p><p>b = 1/2&nbsp;</p><p>&nbsp;</p><p>Substitusikan b ke persamaan (i)&nbsp;</p><p>a + 2b = -4 1/2&nbsp;</p><p>a + 2(1/2) = -4 1/2&nbsp;</p><p>a + 1 = -4 1/2&nbsp;</p><p>a = (-4 1/2) - 1&nbsp;</p><p>a = -5 1/2&nbsp;</p><p>&nbsp;</p><p>Substitusikan a dan b ke rumus umum suku ke-n&nbsp;</p><p>Un = a + (n - 1)b&nbsp;</p><p>Un = -5 1/2 + (n - 1)(1/2)&nbsp;</p><p>Un = -5 1/2 + n/2 - 1/2&nbsp;</p><p>Un = -((2 . 5) + 1)/2 + n/2 - 1/2&nbsp;</p><p>Un = -11/2 -1/2 + n/2&nbsp;</p><p>Un = -12/2 + n/2&nbsp;</p><p>Un = -6 + n/2&nbsp;</p><p>&nbsp;</p><p>Jadi, nilai a = -5 1/2 , b = 1/2 dan Un = -6 + n/2.</p>