document.write( "Question 1190438: A quadratic pattern has a second term equal to 1 a third term equal to -6 and a fifth term equal to -14
\n" ); document.write( "1.1 Calculate the second difference of this quadratic pattern
\n" ); document.write( "1.2 Hence or otherwise calculate the first term of the pattern \n" ); document.write( "

Algebra.Com's Answer #822061 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "

\r\n" );
document.write( "   ___   1     -6       x        -14     the given 2nd, 3rd, and 5th terms, and the unknown 4th term\r\n" );
document.write( "      ___   -7    x+6      -14-x         the first differences\r\n" );
document.write( "         ___  x+13   -2x-20              the second differences\r\n" );
document.write( "\r\n" );
document.write( "In a quadratic sequence, the second differences are constant\r\n" );
document.write( "\r\n" );
document.write( "x+13=-2x-20\r\n" );
document.write( "3x=-33\r\n" );
document.write( "x=-11\r\n" );
document.write( "\r\n" );
document.write( "Rewrite the array using x=-11; and show the constant second difference\r\n" );
document.write( "\r\n" );
document.write( "   ___   1     -6      -11        -14\r\n" );
document.write( "      ___   -7     -5        -3\r\n" );
document.write( "          2     2       2\r\n" );
document.write( "\r\n" );
document.write( "Work back up the array to find the first term of the sequence\r\n" );
document.write( "\r\n" );
document.write( "    10   1     -6      -11        -14\r\n" );
document.write( "       -9    -7     -5        -3\r\n" );
document.write( "          2     2       2

\n" ); document.write( "ANSWERS:
\n" ); document.write( "1.1 The constant second difference is 2
\n" ); document.write( "1.2 The first term is 10
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );