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Sequence - Summation and General term

SOURCE:COMPETITION
Number of Problems: 5.
FOR PRINT ::: (Book)

Problem Num : 1
Type: Understanding
Topic:Sequence 
Theme:Manipulation
Adjustment# :
Difficulty: 2

Category Summation and General term
Analysis
Solution/Hint


Problem Num : 2
Type: Understanding
Topic:Sequence 
Theme:None
Adjustment# :
Difficulty: 2

Category Summation and General term
Analysis
Solution/Hint


Problem Num : 3
Type: None
Topic:Sequence 
Theme:None
Adjustment# :
Difficulty: 1

Category Summation and General term
Analysis
Solution/Hint


Problem Num : 4
Type: Understanding
Topic:Sequence 
Theme:Pattern
Adjustment# :
Difficulty: 3

Category Summation and General term
Analysis
Solution/Hint


Problem Num : 5
Type:
Topic:Sequence 

Adjustment# : 0
Difficulty: 1
'

For each positive integer n, the mean of the first n terms of a sequence is n. What is the 2008th term of the sequence?

mathrm{(A)} {{{2008}}} qquad mathrm{(B)} {{{4015}}} qquad mathrm{(C)} {{{4016}}} qquad mathrm{(D)} {{{4,030,056}}}...

'
Category Summation and General term
Analysis
Solution/Hint

Since the mean of the first n terms is n, the sum of the first n terms is n^2. Thus, the sum of the first 2007 terms is 2007^2 and the sum of the first 2008 terms is 2008^2. Hence, the 2008th term is 2008^2-2007^2=(2008+2007)(2008-2007)=4015Rightarrow oxed{B}

Note that n^2 is the sum of the first n odd numbers.