<PRE><B>Question 610800</B>
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.&lt;P&gt;

9-3 = 6&lt;BR&gt;
21-9 = 12&lt;BR&gt;
46-21 = 25&lt;BR&gt;
91-46 = 45&lt;br&gt;
163-91 = 72&lt;br&gt;
269-163 = 106&lt;P&gt;
Now check the difference between those differences (second differences).&lt;P&gt;
12-6 = 6&lt;BR&gt;
25-12 = 13&lt;BR&gt;
45-25 = 20&lt;BR&gt;
72-45 = 27 &lt;BR&gt;
106-72 = 34&lt;BR&gt;
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.&lt;P&gt;

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