document.write( "Question 610800: what is the next numbers in a series of 3,9,21,46,91,163, 269 \n" ); document.write( "
Algebra.Com's Answer #384600 by fcabanski(1391)\"\" \"About 
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This sequence appears to change by a second or third difference. That is, the difference between the numbers in the sequence change by a certain difference, that itself may change by a certain amount. To determine the differences, find the differences between the numbers in the sequence.

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\n" ); document.write( "\n" ); document.write( "9-3 = 6

\n" ); document.write( "21-9 = 12

\n" ); document.write( "46-21 = 25

\n" ); document.write( "91-46 = 45

\n" ); document.write( "163-91 = 72

\n" ); document.write( "269-163 = 106


\n" ); document.write( "Now check the difference between those differences (second differences).


\n" ); document.write( "12-6 = 6

\n" ); document.write( "25-12 = 13

\n" ); document.write( "45-25 = 20

\n" ); document.write( "72-45 = 27

\n" ); document.write( "106-72 = 34

\n" ); document.write( "Notice that the second difference increases by 7 each time. So the next second difference is 41. 106+41=147. 269+147=416, the next number in the sequence.

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\n" ); document.write( "\n" ); document.write( "Contact me for private tutoring - fcabanski@hotmail.com
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