2006-09-01 05:51:29 · 11 answers · asked by Kansas 2 in Science & Mathematics ➔ Mathematics
358, 537, 766, 1051, 1398 and so on.
2006-09-01 05:57:51 · answer #1 · answered by Nacho Massimino 6 · 2⤊ 0⤋
Your series can be predicted with the polynomial:
x^3 - 2x^2 -4x +6.
This polynomial satisfies all of the elements of your series and predicts the next element to be: 358.
I arrived at the idea that it would take a 3rd degree polynomial by using the differencing technique on your sequence. After 3 levels of looking at the differences of the resulting sequence (i.e., the difference of the difference sequence), it resulted in a zero sequence. This implies that a 3rd degree polynomial will work for the sequence.
Then, I created 4 equations with 4 unknown from a generic polynomial: y = ax^3 + bx^2 + cx + d
and put in x=1, 2, 3, 4 and knowing that y would be 1, -2, 3, 22.
Solving the 4x4 system gave the coefficients of 1, -2, -4, and 6.
The polynomial correctly predicted all the other members of the sequence.
However, an easier way of just getting the next element can be found from just using the differencing technique:
1, -2, 3, 22, 61, 126, 223 results in
-3...5...19...29...65...97
...8...14...20...26...32
K, you can see the pattern in the 3 row, so, the next number in the 3rd row will be 38.
38 added to 97 will give you 135 as the next number in the 2nd row.
And, 135 added to 223 will give you 358 as your next number.
2006-09-01 07:11:26 · answer #2 · answered by tbolling2 4 · 1⤊ 0⤋
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2016-10-15 22:32:35 · answer #3 · answered by ? 4 · 0⤊ 0⤋
358
2006-09-01 06:11:55 · answer #4 · answered by naturelover 3 · 1⤊ 0⤋
358, 537
2006-09-01 05:59:47 · answer #5 · answered by Anonymous · 1⤊ 0⤋
358 537 766....
solutions of x^3-2x^2-4x+6
2006-09-01 07:11:22 · answer #6 · answered by monarca_08 1 · 1⤊ 0⤋
The next number should be 261 and the next one after that should be 305
2006-09-01 05:57:09 · answer #7 · answered by Shadow 3 · 0⤊ 0⤋
662
2006-09-01 06:03:52 · answer #8 · answered by iyiogrenci 6 · 0⤊ 1⤋
445
2006-09-01 05:56:32 · answer #9 · answered by Anonymous · 0⤊ 1⤋
436??
2006-09-01 05:55:33 · answer #10 · answered by A 4 · 0⤊ 1⤋