SOLUTION: what is the next numbers in a series of 3,9,21,46,91,163, 269

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): You can put this solution on YOUR website!
416
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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