Question 610800: what is the next numbers in a series of 3,9,21,46,91,163, 269
Found 2 solutions by richwmiller, fcabanski:
Answer by richwmiller(17219)   (Show Source):
Answer by fcabanski(1391)  (Show Source):
You can put this solution on YOUR website! 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.
9-3 = 6
21-9 = 12
46-21 = 25
91-46 = 45
163-91 = 72
269-163 = 106
Now check the difference between those differences (second differences).
12-6 = 6
25-12 = 13
45-25 = 20
72-45 = 27
106-72 = 34
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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