document.write( "Question 177700: I know there is a simpler way of doing this problem other than replacing the variable with each consecutive integer until they add up to 300, because I tried that and they didn't add up. I would appreciate any help with this problem.
\n" ); document.write( "\"The sum of the consecutive integers 1,2,3, ..., n is given by the formula $\"%281%2F2%29%2An%28n%2B1%29\"$ . How many consecutive integers, starting with 1, must be added to get a sum of 300?\" \n" ); document.write( "

Algebra.Com's Answer #132701 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
S(n) = (1/2)*n(n+1). How many consecutive integers, starting with 1, must be added to get a sum of 300?
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\n" ); document.write( "Equation:
\n" ); document.write( "(n/2)(n+1) = 300
\n" ); document.write( "Multiply both sides by 2 to get:
\n" ); document.write( "n(n+1) = 600
\n" ); document.write( "n^2 +n - 600 = 0
\n" ); document.write( "(n-25)(n+24) = 0
\n" ); document.write( "Positive solution:
\n" ); document.write( "n = 25
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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