Difference between revisions of "2009 AMC 12A Problems/Problem 7"
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== Solution == | == Solution == | ||
| − | As this is an arithmetic sequence, the difference must be constant: <math>(5x-11) - (2x-3) = (3x+1) - (5x-11)</math>. This solves to <math>x=4</math>. The first three terms then are <math>5</math>, <math>9</math>, and <math>13</math>. In general, the <math>n</math> | + | As this is an arithmetic sequence, the difference must be constant: <math>(5x-11) - (2x-3) = (3x+1) - (5x-11)</math>. This solves to <math>x=4</math>. The first three terms then are <math>5</math>, <math>9</math>, and <math>13</math>. In general, the <math>n</math>th term is <math>1+4n</math>. Solving <math>1+4n=2009</math>, we get <math>n=\boxed{502}</math>. |
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== See Also == | == See Also == | ||
Latest revision as of 10:17, 9 February 2015
Problem
The first three terms of an arithmetic sequence are 
, 
, and 
respectively. The 
th term of the sequence is 
. What is ?
Solution
As this is an arithmetic sequence, the difference must be constant: 
. This solves to 
. The first three terms then are 
, 
, and 
. In general, the th term is 
. Solving 
, we get 
.
See Also
| 2009 AMC 12A (Problems • Answer Key • Resources) | |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
