2. 外语
  3. The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n > 3, the nth term in the s

The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n > 3, the nth term in the s

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问题 The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n > 3, the nth term in the sequence is the average(arithmetic mean)of the first n - 1 terms in the sequence. What is the value of the 6th term in the sequence?
Give your answer as a fraction.
选项
答案3/2
解析 For all integers n > 3, the nth term in the sequence is the average of the first n - 1 terms in the sequence.
The 3rd term, which is the average of the first 2 terms, is, or 1.5.
The 4th term, which is the average of the first 3 terms, is, or 1.5.
Similarly, the 5th term is, or 1.5, and the 6th term is, or 1.5. Since you must give your answer as a fraction, the correct answer is 3/2.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 7: Find a Pattern
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