2011 AMC 10A Problems/Problem 4
Contents
Problem
Let X and Y be the following sums of arithmetic sequences:
What is the value of Y - X?
Solution 1
We see that both sequences have equal numbers of terms, so reformat the sequence to look like:
From here it is obvious that Y - X = 102 - 10 = .
Note
Another way to see this is to let the sum So, the sequences become
Like before, the difference between the two sequences is
Solution 2
We see that every number in Y's sequence is two more than every corresponding number in X's sequence. Since there are 46 numbers in each sequence, the difference must be:
See Also
2011 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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