5, 10, 17, 26, 37, ...

I see the pattern, but I can't figure out the equation...any advice?

Printable View

- Mar 12th 2009, 11:53 PMjzelltNumber sequence
5, 10, 17, 26, 37, ...

I see the pattern, but I can't figure out the equation...any advice? - Mar 13th 2009, 12:29 AMu2_wa
Hello

**jzellt:**You might have noticed that difference between the numbers in sequence corresponds to the odd numbers sequence starting from 5.

Now we can write it as

We can use this formula for the addition of the odd numbers:

Lets plug in the values:

(because at n=1, there should be addition of zero i.e**5+0**,5+5,....)

Hence we have the equation:

Hope this helps - Mar 13th 2009, 05:09 AMSoroban
Hello, jzellt!

I "eyeballed" the solution . . .

Quote:

Take the differences of consecutive terms.

Then take the differences of the differences ... and so on.

. .

We see that thedifferences are constant.*second*

This indicates that the generating function is of thedegree, a quadratic.*second*

. . That is, contains

With that in mind, I looked the sequence again, and I saw:

. .

. . .

Therefore: .

. . which verifies u2_wa's result.