Dãy số, tổng hữu hạn, hàm mũ và logarit
ACT Chủ đề 12 4:58 Giọng đọc tiếng Anh · phụ đề tiếng Anh + 中文 được ghi trực tiếp
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Arithmetic sequence: a sub n equals a sub 1 plus n minus 1, times d.
等差数列：a_n = a_1 + (n-1)d。
Its sum is S sub n equals n, times a sub 1 plus a sub n, all over 2.
其前n项和为S_n = n(a_1 + a_n)/2。
Geometric sequence: a sub n equals a sub 1, times r to the power of n minus 1, and S sub n equals a sub 1, times 1 minus r to the power of n, all over 1 minus r, for r not equal to 1.
等比数列：a_n = a_1 r^(n-1)，且当r ≠ 1时，S_n = a_1(1-r^n)/(1-r)。
A logarithm reverses exponentiation: log base b of a equals c means b to the power of c equals a, with a greater than 0, b greater than 0, and b not equal to 1.
对数运算与指数运算互为逆运算：log_b a = c 表示b^c = a，其中a > 0，b > 0，且b ≠ 1。
Each task gives its own data.
每个任务都有各自的数据。
Do not copy the worked example’s numbers.
请勿照搬示例中的数值。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道练习再继续。
Use the full context on the preceding pages.
请结合前几页的完整背景信息作答。
The constant difference is 4 seats per row.
公差是每排四个座位。
The eighth term is a 1 plus 7 d, which is 12 plus 7 times 4, or 40 seats.
第八项等于首项加七倍公差，即十二加七乘四，等于四十个座位。
The sum of eight terms is 8 times 12 plus 40, over 2, which is 208 seats.
前八项的和等于八乘十二加四十再除以二，等于二百零八个座位。
This assumes the same four-seat increase through all eight rows.
这里假定八排都按同样的四个座位递增。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道练习再继续。
Use the full context on the preceding pages.
请结合前几页的完整背景信息进行解答。
The fifth term is a 1 times r to the fourth, which is 5 times 3 to the fourth, or 405.
第五项等于首项乘公比的四次方，即五乘三的四次方，等于四百零五。
The sum of five terms is a 1 times one minus r to the fifth, over one minus r, which is 5 times one minus 243, over one minus 3, or 605.
前五项的和等于首项乘一减公比的五次方，再除以一减公比，即五乘一减二百四十三，除以一减三，等于六百零五。
When r equals 1, the fraction has a zero denominator, and the correct sum is n times a 1, here 25 for five identical terms.
当公比等于一时，这个分式的分母为零，正确的和是 n 乘首项，这里五个相同的项之和是二十五。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
The domain requires x greater than 3.
定义域要求 x 大于三。
The exponential form gives x minus 3 equals 32, so x equals 35, and the argument is positive.
改写成指数形式得到 x 减三等于三十二，所以 x 等于三十五，真数为正。
The sum of logs corresponds to the product 3 x, not x plus 3; at x equals 1, the proposed equality would equate 2 with log base 2 of 3.
对数之和对应的是乘积三 x，而不是 x 加三；当 x 等于一时，所说的等式会让二等于以二为底三的对数。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请结合前几页的完整背景信息作答。
N of t equals 120 times 1.5 to the power t over 2 cells.
N(t) 等于一百二十乘一点五的二分之 t 次方个细胞。
N of 4 is 120 times 1.5 squared, which is 270 cells.
N(4) 等于一百二十乘一点五的平方，即二百七十个细胞。
The growth is 50 percent per two hours, not 150 percent; the four-hour factor is 2.25.
增长率是每两小时百分之五十，而不是百分之一百五十；四小时的增长倍数是二点二五。
The hourly factor would be the square root of 1.5.
每小时的倍数是根号一点五。
Return to the task and explain why the method fits.
请返回该练习，并解释为何此方法适用。
Original practice does not predict an official score.
原始练习成绩无法预测正式评分。
Complete required live or recorded evidence separately.
需单独完成必要的现场或录制证据。
Pause and test yourself. Cover the worked answer, rebuild the answer to the last example in your own words, and name one condition that would change it before you check.
暂停一下，自我检测：遮住示范答案，用自己的话重做最后一个例子的答案，并在核对之前说出一个会改变结论的条件。