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2008 AMC 10B Problem 13

Problem 13 of 25IntermediateAlgebraProbability & Statistics

For each positive integer n,n, the mean of the first nn terms of a sequence is n.n. What is the 20082008th term of the sequence?

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Solution

Since the mean of the first nn terms is n,n, their sum is n2.n^2. The nnth term is n2−(n−1)2=2n−1,n^2-(n-1)^2=2n-1, so the 20082008th term is 2⋅2008−1=4015.2\cdot 2008-1=4015. Thus, the correct answer is B.
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Tagged: mean · summation · algebraic manipulation

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