Difference between revisions of "2007 Alabama ARML TST Problems/Problem 9"
(New page: ==Problem== Let <math>F_1=F_2=1</math>, and <math>F_{n+2}=F_{n+1}+F_n</math> for <math>n\geq 1</math>. Find the value of <math>k</math> such that <math>x=F_k</math> is the <math>x</math>-c...) |
(→See also) |
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==See also== | ==See also== | ||
− | + | {{ARML box|year=2007|state=Alabama|num-b=8|num-a=10}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] |
Revision as of 09:23, 18 June 2008
Problem
Let , and for . Find the value of such that is the -coordinate of the intersection between the linear equations
Solution
We subtract equations:
We can see the pattern:
Thus
Therefore and .
See also
2007 Alabama ARML TST (Problems) | ||
Preceded by: Problem 8 |
Followed by: Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |