How can I compute the Nth term of this series? I've got a sequence defined as such:


*

*between 0 and 5, $i = 1$

*between 6 and 10, $i = 1*d$

*between 11 and 15, $i = 1*d^2$

*between 16 and 20, $i = 1*d^3$

*...


I guess I could write it like this for n=5:
between $k(n)+1$ and $(k+1)n$, $i= 1*d^k$
and I'm looking for the nth term of the induced serie. (ie the sum of the Nth first terms of my sequence)
Actually, I'm trying to solve a real-world problem here. We're selling products with a progressive discount (eg the first 5 items are at full price, then the 5 following items have a 10% discount, then there's an extra 10 percent discount for the next clip of 5, etc).
So far I'm handling this kind of manually (basically, I've created a table with all the possible values up to 1000 - we're not selling Lamborghini's, but still we don't expect a single customer to buy more than 1000 item from us, ever), and I'm quite curious to know how one would solve this using a single math formula.

The sequence is $$d^{\lfloor (n-1)/5 \rfloor}, \text{ } n=1,2,3,\dots$$ See http://en.wikipedia.org/wiki/Floor_and_ceiling_functions. Note I didn't include $n=0$ because that doesn't fit the pattern of the rest of your sequence. (There are 6 numbers between 0 and 5 exclusive, unlike 5 numbers in all the other intervals.)
