Help with number pattern

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Beachman69

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Sep 15, 2009
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My Child brought home home work that confuses me!!!! Please Help
the question is analyze patterns

1,3,4 (space)2,5,7(space) 8,9,17(space) 25,30,?(space) ?,?,?

We have found the first and second add up to the third but unable to find the continuing digits
The whole neighborhood is dumbstruck.

sorry for the confusion
 


The exercise might have picked up a typographical error somewhere along the "way" from conception to your child's dinner plate.

I see no obvious pattern.

If your child is sure that the given sequence is 1, 3, 4, 2, 5, 7, 8, 9, 17, 25, 30, … , then have them report the next four numbers as 1527, 16445, 99815, 441990.

If the teacher asks why, then have your child say, "This is based on an 11th-degree polynomial function with Rational coefficients whose restricted domain consists of the Natural numbers".

Heh, heh. :p

It looks like this.

\(\displaystyle y \;=\; \frac{767}{39916800} \cdot x^{11} \;-\; \frac{71}{60480} \cdot x^{10} \;+\; \frac{4547}{145152} \cdot x^9 \;-\; \frac{19321}{40320} \cdot x^8 \;+\; \frac{5604797}{1209600} \cdot x^7 \;-\ \frac{2825}{96} \cdot x^6 \;+\)

\(\displaystyle \frac{17907797}{145152} \cdot x^5 \;-\; \frac{40374647}{120960} \cdot x^4 \;+\; \frac{499257853}{907200} \cdot x^3 \;-\; \frac{1649113}{3360} \cdot x^2 \;+\; \frac{982031}{5544} \cdot x\)

where y is a number in the given sequence, and x is that particular number's position in the sequence.

For example, in the given sequence, the number 7 is the 6th number.

So, when x = 6, then y turns out to be 7.

When x = 10, then y = 25, and 25 is the 10th number in the sequence.

That's how the polynomial function generates the numbers; we substitute the position number in place of the symbol x, then do all of the arithmetic, and the result (y) is the number in the sequence at that particular position x.

If you plug in x = 12, then you get the 12th number: y = 1527.

When x = 13, the 13th number is y = 16445.

x = 14, y = 99815.

x = 15, y = 441990.

(Heh, heh, heh …)

Seriously, I'd check the accuracy of the given information. Somebody might have goofed.

 
Hello, Beachman69!

mmm444bot gave an imaginative (and amusing) solution.
. . Here's mine . . .

The question is analyze the pattern.

. . \(\displaystyle 1,3,4,\quad 2,5,7, \quad 8,9,17, \quad 25,30, \_\_\:, \quad \_\_\:,\: \_\_\:,\: \_\_\)

We have found the first and second add up to the third, but unable to find the continuing digits.
The whole neighborhood is dumbstruck.
Click to expand...

\(\displaystyle \text{The sequence occurs in sets-of-3: }\;(a,b,c) \;=\;(1,3,4),\;(2,5,7),\;(8,9,17),\;(25,30,55),\:\hdots\)


\(\displaystyle \text{The }a\text{'s have the sequence: }{\:1, 2, 8, 25,\hdots\)

. . \(\displaystyle \text{These are generated by: }\:a(n) \;=\;\frac{2n^3 - 7n^2 + 9n - 2}{2}\)


\(\displaystyle \text{The }b\text{'s have the sequence: }\:3, 5, 9, 30, \hdots\)

. . \(\displaystyle \text{These are generated by: }\:b(n) \;=\;\frac{5n^3 - 28n^2 + 53n - 24}{2}\)


\(\displaystyle \text{The }c\text{'s are the sums of the respective }a\text{'s and }b\text{'s.}\)

. . \(\displaystyle \text{These are generated by: }\:c(n) \;=\;\frac{7n^3 - 35n^2 + 62n - 26}{2}\)


\(\displaystyle \text{The next set is: }\;\bigg[a(5), b(5), c(5)\bigg] \;=\;\bigg(59,\:83,\:142\bigg)\)

 


Oh, I missed the spaces.

Anyway, Beach Man, is the verdict in, yet ?

 
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