I was asked the following:
Determine a formula for the following sum with $n\in\mathbb N$:
$$S=2+7+12+\cdots+(5n-3)$$
I had no clue about what to do about it. I just wrote, for the sake of doing something, the following:
$$\sum_{i=0}^n(5i-3) = \left(\sum_{i=0}^n(5i) - 3n\right)$$
Curiously, I got a few points for that. But eventually, there is an annotation by the professor:
And?
So apparently I was on the right path. What was I supposed to do afterward? How do you "make up a formula" of a given sum?