Hướng dẫn giải Bài 8 (Trang 107 SGK Toán Đại số & Giải tích 11)

Tìm số hạng đầu <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub></math> và công sai d của các cấp số cộng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>u</mi><mi>n</mi></msub></mfenced><mo>,</mo></math> biết: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>5</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>10</mn><msub><mi>u</mi><mn>5</mn></msub><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>S</mi><mn>4</mn></msub><mo>=</mo><mn>14</mn><mo> </mo><mo>;</mo><mo> </mo></mtd></mtr></mtable></mfenced></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>7</mn></msub><mo>+</mo><msub><mi>u</mi><mn>15</mn></msub><mo>=</mo><mn>60</mn></mtd></mtr><mtr><mtd><msubsup><mi>u</mi><mn>4</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>u</mi><mn>12</mn><mn>2</mn></msubsup><mo>=</mo><mn>1170</mn><mo>.</mo></mtd></mtr></mtable></mfenced></math> Giải Áp dụng <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mi>d</mi><mo> </mo><mi>v</mi><mi>à</mi><mo> </mo><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><mfrac><mrow><mi>n</mi><mfenced open="[" close="]"><mrow><mn>2</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mi>d</mi></mrow></mfenced></mrow><mn>2</mn></mfrac></math> a) Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mn>5</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>10</mn><msub><mi>u</mi><mn>5</mn></msub><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>S</mi><mn>4</mn></msub><mo>=</mo><mn>14</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mn>5</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>10</mn><mfenced><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>4</mn><mi>d</mi></mrow></mfenced><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mfrac><mrow><mn>4</mn><mfenced><mrow><mn>2</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>3</mn><mi>d</mi></mrow></mfenced></mrow><mn>2</mn></mfrac><mo>=</mo><mn>14</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mn>3</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>8</mn><mi>d</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>3</mn><mi>d</mi><mo>=</mo><mn>7</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>8</mn></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></mrow></mfenced></mrow></mfenced></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>7</mn></msub><mo>+</mo><msub><mi>u</mi><mn>15</mn></msub><mo>=</mo><mn>60</mn></mtd></mtr><mtr><mtd><msubsup><mi>u</mi><mn>4</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>u</mi><mn>12</mn><mn>2</mn></msubsup><mo>=</mo><mn>1170</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>6</mn><mi>d</mi><mo>+</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>14</mn><mi>d</mi><mo>=</mo><mn>60</mn></mtd></mtr><mtr><mtd><msup><mfenced><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>3</mn><mi>d</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>11</mn><mi>d</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>1170</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math>                                  <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>10</mn><mi>d</mi><mo>=</mo><mn>30</mn></mtd></mtr><mtr><mtd><msubsup><mi>u</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><mn>14</mn><msub><mi>u</mi><mn>1</mn></msub><mi>d</mi><mo>+</mo><mn>65</mn><msup><mi>d</mi><mn>2</mn></msup><mo>=</mo><mn>585</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mo>-</mo><mn>12</mn></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mfrac><mn>21</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></mrow></mfenced></mrow></mfenced></math>

Hướng dẫn Giải Bài 8 (trang 107, SGK Toán Đại số & Giải Tích 11)

GV:

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