Difference between revisions of "1999 AHSME Problems/Problem 20"
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Revision as of 11:37, 9 January 2017
Problem
The sequence statisfies , and, for all , is the arithmetic mean of the first terms. Find .
Solution
Let be the arithmetic mean of and . We can then write and for some .
By definition, .
Next, is the mean of , and , which is again .
Realizing this, one can easily prove by induction that .
It follows that . From we get that . And thus .
See also
1999 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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