document.write( "Question 1195799: What is the next number in this series ?
\n" ); document.write( "Series : 1, 54, 375, 1372, 3645, ?
\n" ); document.write( "Looking forward to your prompt and positive reply 🙂 \n" ); document.write( "

Algebra.Com's Answer #828355 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "As the other tutor said, any problem like this is nonsense if you are expected to get the \"right\" answer.

\n" ); document.write( "However, in ANY problem like this, you can get AN answer that is mathematically justifiable by assuming the given sequence is formed by a polynomial equation. In that case, you can find \"A\" next number using the method of finite differences.

\n" ); document.write( "The given sequence has 5 terms, so there is a unique polynomial of degree 4 that produces the sequence. And in that polynomial of degree 4, the 4th differences are constant. (If you know some basic calculus, that is saying that the 4th derivative of a polynomial of degree 4 is a constant.)

\n" ); document.write( "Use the method of finite differences to find the constant 4th difference

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document.write( "   1      54      375     1372      3645\r\n" );
document.write( "       53     321     997      2273\r\n" );
document.write( "          268     676     1276\r\n" );
document.write( "              408     600\r\n" );
document.write( "                  192\r\n" );
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document.write( "The constant 4th difference is 192.  Use that constant difference to build back up the array to find the next number in the sequence.\r\n" );
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document.write( "   1      54      375     1372      3645      7986\r\n" );
document.write( "       53     321     997      2273      4341\r\n" );
document.write( "          268     676     1276      2068\r\n" );
document.write( "              408     600       792\r\n" );
document.write( "                  192      192\r\n" );
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\n" ); document.write( "The next number in the sequence, assuming a polynomial of degree 4, is 7986.

\n" ); document.write( "That is one of the answer choices; so apparently this sequence is a polynomial sequence.

\n" ); document.write( "Some of the other sequences at the URL referenced by the other tutor MIGHT be polynomial sequences, but others might not.

\n" ); document.write( "In the end, you can NEVER know if any answer you get to a problem like this is the \"right\" answer.
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