document.write( "Question 1108399: -3, -2, x, -6, y................is a quadratic sequence.
\n" ); document.write( "determine the value of x and y. \n" ); document.write( "

Algebra.Com's Answer #723431 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The solution by the other tutor is a perfectly good one, using a standard algebraic technique. Here is another method that is often useful on problems like this.

\n" ); document.write( "In any quadratic sequence, the row of \"second differences\" is constant. Here is an example.

\n" ); document.write( "For f(x) = 2x^2+3x-4, the first few terms of the sequence are
\n" ); document.write( "1, 10, 23, 40, 61
\n" ); document.write( "The \"first differences\" (differences between successive terms of the sequence) ar
\n" ); document.write( "9, 13, 17, 21
\n" ); document.write( "The \"second differences\" (differences between successive first differences) are
\n" ); document.write( "4, 4, 4

\n" ); document.write( "This will always be the case for a quadratic sequence.

\n" ); document.write( "So we can apply this knowledge to solving your problem.

\n" ); document.write( "The terms of your sequence are
\n" ); document.write( "-3, -2, x, -6, y
\n" ); document.write( "The first differences are
\n" ); document.write( "1, x+2, -6-x, y+6
\n" ); document.write( "The second differences are
\n" ); document.write( "x+1, -2x-8, x+y+12

\n" ); document.write( "Since we know the second differences are constant, we have
\n" ); document.write( " $\"x%2B1+=+-2x-8\"$
\n" ); document.write( " $\"3x+=+-9\"$
\n" ); document.write( " $\"x+=+-3\"$

\n" ); document.write( "Then
\n" ); document.write( " $\"-2x-8+=+x%2By%2B12\"$
\n" ); document.write( " $\"6-8+=+-3%2By%2B12\"$
\n" ); document.write( " $\"-2+=+y%2B9\"$
\n" ); document.write( " $\"-11+=+y\"$

\n" ); document.write( "As found by the other tutor, the missing numbers are x = -3 and y = -11. \n" ); document.write( "

\n" );