Difference between revisions of "2009 AMC 12A Problems/Problem 7"

(New page: == Problem == The first three terms of an arithmetic sequence are <math>2x - 3</math>, <math>5x - 11</math>, and <math>3x + 1</math> respectively. The <math>n</math>th term of the sequence...)
 
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Revision as of 20:42, 3 July 2013

Problem

The first three terms of an arithmetic sequence are $2x - 3$, $5x - 11$, and $3x + 1$ respectively. The $n$th term of the sequence is $2009$. What is $n$?

$\textbf{(A)}\ 255 \qquad \textbf{(B)}\ 502 \qquad \textbf{(C)}\ 1004 \qquad \textbf{(D)}\ 1506 \qquad \textbf{(E)}\ 8037$

Solution

As this is an arithmetic sequence, the difference must be constant: $(5x-11) - (2x-3) = (3x+1) - (5x-11)$. This solves to $x=4$. The first three terms then are $5$, $9$, and $13$. In general, the $n$-th term is $1+4n$. Solving $1+4n=2009$ we get $n=\boxed{502}$.


See Also

2009 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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