No, I didn't try induction. The reason is that this chapter is before induction in the textbook, and we didn't cover induction in class untill after the work was set. I suppose it's worth a try though.
But I still can't see a way of applying it to this question specifically.
You can write each odd number as 2k-1 and each even number as 2k and then apply this formula. Then you can add and subtract suitable terms to bring it to the required form.