document.write( "Question 962492: Set A consists of the numbers in the arithmetic sequence 15, 24, 33.... and Set B consists of the numbers in the arithmetic sequence 21, 27, 33.... What is the sum of the five smallest numbers common to both sets? \n" ); document.write( "

Algebra.Com's Answer #590124 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Set A consists of the numbers in the arithmetic sequence 15, 24, 33.... and Set
\n" ); document.write( "B consists of the numbers in the arithmetic sequence 21, 27, 33.... What is the
\n" ); document.write( "sum of the five smallest numbers common to both sets?
\n" ); document.write( "

\r\n" );
document.write( "The common difference of sequence A is 6\r\n" );
document.write( "The common difference of sequence B is 9\r\n" );
document.write( "\r\n" );
document.write( "Their smallest common number is 33, since we see that's the 3rd number\r\n" );
document.write( "in each sequence. The sequences will have the next common term when we\r\n" );
document.write( "have added enough 6's to 33 in A and enough 9's to 33 in B so that the\r\n" );
document.write( "number of 6's added in A and the number of 9's added in B will be a\r\n" );
document.write( "multiple of both 6 and 9, or a multiple of 18. Therefore, the sequence \r\n" );
document.write( "of common terms will have first term 33, and common difference 18, the \r\n" );
document.write( "LCM of 6 and 9.\r\n" );
document.write( "\r\n" );
document.write( "So the first five terms of the sequence of numbers common to both sets \r\n" );
document.write( "is 33, 51, 69, 87, 105.  Their sum is 345.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );