Difference between revisions of "2008 AMC 10B Problems/Problem 10"
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==Problem== | ==Problem== | ||
− | {{ | + | Suppose that <math>(u_n)</math> is a serquence of real numbers satifying <math>u_{n+2}=2u_{n+1}+u_n</math>, |
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+ | and that <math>u_3=9</math> and <math>u_6=128</math>. What is <math>u_5</math>? | ||
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+ | (A) 40 (B) 53 (C) 68 (D) 88 (E) 104 | ||
==Solution== | ==Solution== | ||
− | {{solution | + | We know that <math>u_6=128</math>, so we plug in <math>n=4</math> to get <math>128=2u_5+u_4</math>. We plug in <math>n=3</math> to get |
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+ | <math>u_5=2u_4+9</math>. Substituting gives | ||
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+ | <math>128=5u_4+18 \rightarrow u_4=22</math> | ||
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+ | This gives <math>u_5=\frac{128-22}{2}=53</math>. | ||
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+ | Answer B is the correct answer | ||
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+ | NOTE: This is my (BOGTRO) solution, not the official one, | ||
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+ | and should be ignored in view of a better solution. | ||
==See also== | ==See also== | ||
{{AMC10 box|year=2008|ab=B|num-b=9|num-a=11}} | {{AMC10 box|year=2008|ab=B|num-b=9|num-a=11}} |
Revision as of 16:26, 10 August 2008
Problem
Suppose that is a serquence of real numbers satifying ,
and that and . What is ?
(A) 40 (B) 53 (C) 68 (D) 88 (E) 104
Solution
We know that , so we plug in to get . We plug in to get
. Substituting gives
This gives .
Answer B is the correct answer
NOTE: This is my (BOGTRO) solution, not the official one,
and should be ignored in view of a better solution.
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 10 Problems and Solutions |