nth terms please help

The last term is 1, 1+3, 4+5, and so on, adding consecutive odd numbers, which is also the pattern for successive perfect squares, so the end term of the nth row is n^2. If you take that logic one step further, you'll see that the first term is one more than the last term of the previous row, so the first term of the nth row is (n-1)^2 + 1. Since the middle term of every row is the average, you just have to multiply the middle term by the number of terms in the nth row. Since the number of terms goes up by two every step, the middle term moves to the right once for ever step (1st, 2nd, 3rd, etc.). So the middle term can be found by taking the last term (n^2) and subtracting (n-1). And the number of terms in a row is just 2n-1. So if you multiply those together, you get (n^2 - n +1)(2n -1) or (2n^3 - 3n^2 + 3n - 1).