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2011 AMC 10A Problem 4

Problem 4 of 25EasierAlgebra

Let XX and YY be the following sums of arithmetic sequences: X=10+12+14+⋯+100,Y=12+14+16+⋯+102.\begin{aligned} X &= 10+12+14+\cdots+100,\\ Y &= 12+14+16+\cdots+102. \end{aligned} What is the value of Y−X?Y - X?

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Solution

Note that the terms 1212 through 100100 are common to both sums. When we subtract, all these terms cancel out. This means that Y−X=102−10=92. Y - X = 102 - 10 = 92. Thus, A is the correct answer.
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Tagged: arithmetic sequence · summation

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