2001 AIME II Problems/Problem 3: Difference between revisions
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== Problem == | == Problem == | ||
Given that | Given that | ||
< | <cmath> | ||
\begin{align*}x_{1}&=211,\\ | |||
x_{2}&=375,\\ | |||
x_{3}&=420,\\ | |||
x_{4}&=523,\ \text{and}\\ | |||
x_{n}&=x_{n-1}-x_{n-2}+x_{n-3}-x_{n-4}\ \text{when}\ n\geq5, \end{align*} | |||
</cmath> | |||
find the value of <math>x_{531}+x_{753}+x_{975}</math>. | find the value of <math>x_{531}+x_{753}+x_{975}</math>. | ||
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Therefore, <math>x_{y}=x_{y-10}</math>, so | Therefore, <math>x_{y}=x_{y-10}</math>, so | ||
<cmath> | |||
<cmath>x_{531}+x_{753}+x_{975}=x_1+x_3+x_5=x_1+x_3+x_4-x_3+x_2-x_1=x_4+x_2=523+420=\boxed{943}</cmath> | \begin{align*}x_{531}+x_{753}+x_{975}=x_1+x_3+x_5&=x_1+x_3+x_4-x_3+x_2-x_1\\ | ||
&=x_4+x_2=523+420=\boxed{943}\end{align*} | |||
</cmath> | |||
== See also == | == See also == | ||
{{AIME box|year=2001|n=II|num-b=2|num-a=4}} | {{AIME box|year=2001|n=II|num-b=2|num-a=4}} | ||
find the value of 
.
, so
