Difference between revisions of "2011 AMC 10A Problems/Problem 4"
(Created page with 'Let X and Y be the following sums of arithmetic sequences: <cmath> \begin{eqnarray*}X &=& 10+12+14+\cdots+100,\\ Y &=& 12+14+16+\cdots+102.\end[eqnarray*} </cmath> What is the…') |
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Revision as of 01:44, 11 February 2011
Let X and Y be the following sums of arithmetic sequences:
\begin{eqnarray*}X &=& 10+12+14+\cdots+100,\\ Y &=& 12+14+16+\cdots+102.\end[eqnarray*} (Error compiling LaTeX. Unknown error_msg)
What is the value of Y - X?
We see that both sequences have equal numbers of terms, so reformat the sequence to look like:
Y =_____12 + 14 + ... + 100 + 102
X = 10 + 12 + 14 + ... + 100
From here it is obvious that