document.write( "Question 637907: three consecutive terms if an AP have sum 21 and product 315.find the three numbers of the arithmetic progression.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #401938 by reviewermath(1029) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let x be the first term and k be the common difference.
\n" ); document.write( "The three consecutive terms of the sequence are x, x + k, and x + 2k.
\n" ); document.write( "sum: 3x + 3k = 21 or x + k = 7 or k = 7 - x
\n" ); document.write( "product: x(x + k)(x + 2k) = 315, substitute k = 7 - x
\n" ); document.write( " x(7)(14 - x) = 315, divide both sides by 7
\n" ); document.write( " $\"x%2814+-+x%29=+45\"$
\n" ); document.write( " $\"x%5E2+-14x+%2B+45+=+0\"$
\n" ); document.write( " $\"%28x+-+5%29%28x+-+9%29+=+0\"$
\n" ); document.write( "If x = 5, then k =2 and the terms of the sequence are 5, 7, and 9.
\n" ); document.write( "If x = 9 then k = -2 and the terms of the sequence are 9, 7, and 5.\r
\n" ); document.write( "\n" ); document.write( "Answer: 5, 7, and 9.
\n" ); document.write( " \n" ); document.write( "

\n" );