5, 10, 17, 26, 37, ...
I see the pattern, but I can't figure out the equation...any advice?
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
I "eyeballed" the solution . . .
Take the differences of consecutive terms.
Then take the differences of the differences ... and so on.
We see that the second differences are constant.
This indicates that the generating function is of the second degree, a quadratic.
. . That is, contains
With that in mind, I looked the sequence again, and I saw:
. . .
. . which verifies u2_wa's result.