document.write( "Question 291098: The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set? \n" ); document.write( "
Algebra.Com's Answer #210586 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The sum of integers from -25 to +25 is obviously 0. The numbers from -25 \r\n" );
document.write( "to -1 makes 25 numbers and the numbers from 1 to 25 makes another 25 numbers.\r\n" );
document.write( "Then the 0 between -1 and +1 makes a 51st number and if we put 26 on the upper\r\n" );
document.write( "end the sum will be 26.  So there must be 52 numbers in the set.\r\n" );
document.write( "\r\n" );
document.write( "But if you're supposed to work it out with an algebraic  formula, \r\n" );
document.write( "then you'll have to do it this way:\r\n" );
document.write( "\r\n" );
document.write( "\"a%5B1%5D=-25\"  \"d=1\",  \"S%5Bn%5D=26\".  Find n\r\n" );
document.write( "\r\n" );
document.write( "Formula needed:\r\n" );
document.write( "\r\n" );
document.write( "\"S%5Bn%5D=%28n%2F2%29%282a%5B1%5D+%2B+%28n-1%29d%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"26=%28n%2F2%29%282%2A%28-25%29+%2B%28n-1%291%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"26=%28n%2F2%29%28-50+%2Bn-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"26=%28n%2F2%29%28-51+%2Bn%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by 2\r\n" );
document.write( "\r\n" );
document.write( "\"52=n%28-51%2Bn%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"52=-51n%2Bn%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"0=n%5E2-51n-52\"\r\n" );
document.write( "\r\n" );
document.write( "Factor the right side:\r\n" );
document.write( "\r\n" );
document.write( "\"0=%28n-52%29%28n%2B1%29\"\r\n" );
document.write( "\r\n" );
document.write( "Setting each factor equal to 0\r\n" );
document.write( "\r\n" );
document.write( "\"n-52=0\" gives \"n=52\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%2B1=0\" gives \"n=-1\"\r\n" );
document.write( "\r\n" );
document.write( "We cannot have a negative number of terms, so\r\n" );
document.write( "\r\n" );
document.write( "There are 52 terms, or numbers in the set.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );