2008 AMC 12B Problems/Problem 12
Problem
For each positive integer , the mean of the first terms of a sequence is . What is the th term of the sequence?
Solution
Letting be the nth partial sum of the sequence:
The only possible sequence with this result is the sequence of odd integers.
Alternate Solution
Letting the sum of the sequence equal yields the following two equations:
and
.
Therefore:
and
Hence, by substitution,
See Also
2008 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 |
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