Should be a simple math problem...

[Rufus T. Firefly]

So I'm helping little Miss Firefly with some homework, and now I'm puzzled.

The question was to find a formula to predict the next number in this sequence:

1, 5, 13...

I found:

xn = (n-1)^2 + n^2

She found:

xn = xn-1 + 4(n-1)

(sorry, I don't know how to do subscripts in vB or html)

The thing is both our formulas not only work, but continue to give yield the same numbers as you go up the sequence, which must mean they're equivalent. But I can't see it. Explain, math gods!

[alva]

(sorry, I don't know how to do _subscripts in ^{vB or html})

I can help you with that one ( not with the math).

< sub > < / sub> // < sup > < / sup >

[Blake]

It's not too hard.
Take your formula and derive the difference between X(n) and X(n-1)
ie
((n-1)^2 + n^2) - ((n-2)^2 + (n-1)^2)

= n^2 - (n-2)^2 <--- expand that
= n^2 - (n^2-4n+4)
= 4n - 4
= 4(n-1)

and there you have it, the difference between x(n) and x(n-1).

hope that makes sense.

[Rufus T. Firefly]

My, but service is prompt around here!

Thanks!

[alva]

So will be the bill.