document.write( "Question 991238: What is the equation to find the 21th number of the sequence: 4, 6, 10, 16, ... \n" ); document.write( "
Algebra.Com's Answer #853951 by MathTherapy(10801)\"\" \"About 
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document.write( "What is the equation to find the 21th number of the sequence: 4, 6, 10, 16, ...\r\n" );
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document.write( "What is the equation to find the 21th number of the sequence: 4, 6, 10, 16, ...\r\n" );
document.write( "The 2nd DIFFERENCES (2) are the same, so we have a QUADRATIC sequence. We then use \r\n" );
document.write( "the quadratic form of an equation to find the required equation. \r\n" );
document.write( "QUADRATIC equation form: \"y+=+Ax%5E2+%2B+Bx+%2B+C\"\r\n" );
document.write( "We can use any 3 points. 1st point is 4, so coordinate point is (x1, y1) = (1, 4)\r\n" );
document.write( "                                            2nd point is 6, so coordinate point is (x2, y2) = (2, 6)\r\n" );
document.write( "                                            3rd point is 10, so coordinate point is (x3, y3) = (3, 10)\r\n" );
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document.write( "                   (1, 4)                                               (2, 6)                                                        (3, 10)\r\n" );
document.write( "       \"system%28y+=+Ax%5E2+%2B+Bx+%2B+C%2C%0D%0A4+=+A%281%29%5E2+%2B+B%281%29+%2B+C%29\"                   \"system%28y+=+Ax%5E2+%2B+Bx+%2B+C%2C%0D%0A6+=+A%282%29%5E2+%2B+B%282%29+%2B+C%29\"                             \r\n" );
document.write( "    4 = A + B + C ---- eq (i)            6 = 4A + 2B + C ---- eq (ii)                  10 = 9A + 3B + C ---- eq (iii)        \r\n" );
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document.write( "      4 =  A +    B + C --- eq (i)\r\n" );
document.write( "      6 = 4A + 2B + C --- eq (ii)\r\n" );
document.write( "    10 = 9A + 3B + C --- eq (iii) \r\n" );
document.write( "      2 = 3A + B ------ Subtracting eq (i) from eq (ii) ---- eq (iv)\r\n" );
document.write( "      4 = 5A + B  ----- Subtracting eq (ii) from eq (iii) --- eq (v)\r\n" );
document.write( "      2 = 2A ----- Subtracting eq (iv) from eq (v)\r\n" );
document.write( "      \"highlight%282%2F2+=+1+=+A%29\"\r\n" );
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document.write( "      2 = 3(1) = B ------ Substituting 1 for A in eq (iv)\r\n" );
document.write( "2 - 3 = B\r\n" );
document.write( "   - 1 = B\r\n" );
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document.write( "     4 = 1 + - 1 + C ---- Substituting 1 for A, and - 1 for B, in eq (i)\r\n" );
document.write( "     4 = C\r\n" );
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document.write( "With A being 1, B being - 1, and C being 4, the equation for this sequence is:\r\n" );
document.write( "\"y+=+Ax%5E2+%2B+Bx+%2B+C\" = \"highlight%28y+=+x%5E2+-+x+%2B+4%29\"\r\n" );
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document.write( "So, the 21st term in this sequence, or \"highlight%28y%5B21%5D%29+=+21%5E2+-+21+%2B+4+=+441+-+21+%2B+4+=+highlight%28424%29%29\"
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