Difference between revisions of "2008 AMC 10B Problems/Problem 11"
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<center><math>u_5=2u_4+9.</math></center> | <center><math>u_5=2u_4+9.</math></center> | ||
| − | This is a system of two equations with two unknowns. Multiplying the second equation by 2 and substituting into the first equation gives <math>128=5u_4+18 \Longrightarrow u_4=22</math>, therefore <math>u_5=\frac{128-22}{2}=53 \longrightarrow \textbf{(B)}</math>. | + | This is a system of two equations with two unknowns. Multiplying the second equation by 2 and substituting into the first equation gives <math>128=5u_4+18 \Longrightarrow u_4=22</math>, therefore <math>u_5=\frac{128-22}{2}=53 \longrightarrow \textbf{\boxed{(B)}}</math>. |
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==See also== | ==See also== | ||
Latest revision as of 15:15, 7 June 2024
Problem
Suppose that 
is a sequence of real numbers satifying 
,
and that 
and 
. What is 
?
Solution
If we plug in 
, we get
By plugging in 
, we get
This is a system of two equations with two unknowns. Multiplying the second equation by 2 and substituting into the first equation gives 
, therefore 
.
See also
| 2008 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
