Rumus Un dari barisan 2,6,12,20,30,…. adalah...

<p>Jawaban: U_n= n² + n</p><p>&nbsp;</p><p>Konsep:</p><p>Barisan bilangan bertingkat :</p><p>U₁, &nbsp;U₂, &nbsp;U₃, &nbsp;U₄, &nbsp;U₅, ...</p><p>&nbsp; &nbsp;+x_{1 &nbsp; &nbsp;}+x_{2 &nbsp;&nbsp;}+x_{3 &nbsp;&nbsp;}+x₄ &lt;---- beda antarsuku tingkat pertama</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;+y_{1 &nbsp; &nbsp;}+y_{2 &nbsp; &nbsp;}+y₃ &lt;------ beda antarsuku tingkat kedua, y₁ = y₂ = y₃</p><p>Rumus suku ke-n adalah U_n = an² + bn + c</p><p>dengan</p><p>1. 2a = y₁</p><p>2. 3a + b = x₁</p><p>3. a + b + c = U₁</p><p>&nbsp;</p><p>Pembahasan:</p><p>Diketahui barisan 2, 6, 12, 20, 30, ...</p><p>Perhatikan perhitungan berikut:</p><p>2, 6, 12, 20, 30, ...</p><p>&nbsp; 4 &nbsp; 6 &nbsp; &nbsp;8 &nbsp; &nbsp;10 ....</p><p>&nbsp; &nbsp; &nbsp;2 &nbsp; &nbsp;2 &nbsp; &nbsp;2 .....</p><p>Sehingga:</p><p>U₁= 2</p><p>x₁= 4</p><p>y₁= 2</p><p>Maka:</p><ul><li>2a = 2<br>a = 2/2<br>a = 1</li><li>3a + b = 4<br>3(1) + b = 4<br>3 + b = 4<br>b = 4 - 3<br>b = 1</li><li>1 + 1 + c = 2<br>2 + c = 2<br>c = 2 - 2<br>c = 0</li><li>Maka:<br>U_n = (1)n² + (1)n + 0<br>U_n= n² + n</li></ul><p>Jadi, rumus U_n dari barisan 2, 6, 12, 20, 30, ... adalah U_n= n² + n.</p>