2008 AMC 10B Problem 13

Problem 13 of 25IntermediateAlgebra

For each positive integer

n,

the mean of the first

n

terms of a sequence is

n.

What is the

2008

th term of the sequence?

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Solution

Since the mean of the first

n

terms is

n,

their sum is

n^2.

The

n

th term is

n^2-(n-1)^2=2n-1,

so the

2008

th term is

2\cdot 2008-1=4015.

Thus, the correct answer is B.

Concepts: mean · summation · algebraic manipulation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.