document.write( "Question 926793: Please help with the following. It would be greatly appreciated! \r
\n" ); document.write( "\n" ); document.write( "Given quadratic pattern:
\n" ); document.write( "4;9;X;37\r
\n" ); document.write( "\n" ); document.write( "Determine X and Tn \n" ); document.write( "

Algebra.Com's Answer #562498 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given quadratic pattern:
\n" ); document.write( " $\"4\"$ ; $\"9\"$ ; $\"x\"$ ; $\"37\"$ \r
\n" ); document.write( "\n" ); document.write( "quadratic: $\"an%5E2+%2B+bn+%2B+c+=+y\"$ if $\"y=T%5Bn%5D\"$ where $\"n\"$ starts with $\"1\"$ , we have\r
\n" ); document.write( "\n" ); document.write( "plug in $\"T%5B1%5D=4\"$ , means first term, $\"n=1\"$
\n" ); document.write( "
\n" ); document.write( " $\"a%281%29%5E2+%2B+b+%2B+c+=+4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a+%2B+b+%2B+c+=+4\"$ ............. [1]\r
\n" ); document.write( "\n" ); document.write( " $\"T%5B2%5D=9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a%282%29%5E2+%2B+2b+%2B+c+=+9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4a+%2B+2b+%2B+c+=+9\"$ .......... [2]\r
\n" ); document.write( "\n" ); document.write( " $\"T%5B4%5D=37\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a%284%29%5E2+%2B+4b+%2B+c+=+37\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"16a+%2B+4b+%2B+c+=+37\"$ ............ [3]\r
\n" ); document.write( "\n" ); document.write( "if you subtract [1] from [2], you get\r
\n" ); document.write( "\n" ); document.write( " $\"4a+%2B+2b+%2B+c-%28a+%2B+b+%2B+c%29+=+9-4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4a+%2B+2b+%2B+c-a+-b+-c+=+5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3a+%2B+b++=+5\"$ .....solve for $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b++=+5-3a\"$ \r
\n" ); document.write( "\n" ); document.write( "and [3] - [2] \r
\n" ); document.write( "\n" ); document.write( " $\"16a+%2B+4b+%2B+c-%284a+%2B+2b+%2B+c%29+=+37-9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"16a+%2B+4b+%2B+c-4a+-2b+-+c+=+28\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"12a+%2B2b+=+28\"$ ................plug in $\"b++=+5-3a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"12a+%2B2%285-3a%29+=+28\"$ ...solve for $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"12a+%2B10-6a+=+28\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6a+=+28-10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6a+=18\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a+=+3\"$ , ...now find $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b++=+5-3%2A3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b++=+5-9\"$ \r
\n" ); document.write( "\n" ); document.write( "so $\"b+=+-4\"$ and .now find $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a+%2B+b+%2B+c+=+4\"$ ............. [1]\r
\n" ); document.write( "\n" ); document.write( " $\"3+-4+%2B+c+=+4\"$
\n" ); document.write( " $\"-1+%2B+c+=+4\"$
\n" ); document.write( " $\"c+=+4%2B1\"$
\n" ); document.write( " $\"c+=+5\"$ \r
\n" ); document.write( "\n" ); document.write( "then third term will be:\r
\n" ); document.write( "\n" ); document.write( " $\"3%283%5E2%29+-+4%283%29+%2B+2+=+x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+20+\"$ \r
\n" ); document.write( "\n" ); document.write( "quadratic pattern:
\n" ); document.write( " $\"4\"$ ; $\"9\"$ ; $\"20\"$ ; $\"37\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"T%5Bn%5D=3n%5E2+-4n+%2B+5+\"$ where $\"n\"$ = $\"1\"$ , $\"2\"$ , $\"3\"$ ,....
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