Difference between revisions of "2009 AMC 12B Problems/Problem 12"
VelaDabant (talk | contribs) (New page: == Problem == The fifth and eighth terms of a geometric sequence of real numbers are <math>7!</math> and <math>8!</math> respectively. What is the first term? <math>\mathrm{(A)}\ 60\qqu...) |
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== See also == | == See also == | ||
{{AMC12 box|year=2009|ab=B|num-b=11|num-a=13}} | {{AMC12 box|year=2009|ab=B|num-b=11|num-a=13}} | ||
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Latest revision as of 10:56, 4 July 2013
Problem
The fifth and eighth terms of a geometric sequence of real numbers are 
and 
respectively. What is the first term?
Solution
Let the 
th term of the series be 
. Because
![\[\frac {8!}{7!} = \frac {ar^7}{ar^4} = r^3 = 8,\]](http://latex.artofproblemsolving.com/4/a/c/4acfa5ec8bb1e8e6fc08dbc68222f4e3c6fa3a4f.png)
it follows that 
and the first term is 
. The answer is 
.
See also
| 2009 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 11 |
Followed by Problem 13 |
| 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. 
