write an expression for the nth term of the sequence.... write an expression for the nth term of the sequence 0, 7, 16, 27, 40 
It is neither geometric or arithmetic 
My teacher gave us a key and I can't read his writing...please any help would be great!!
 A: HINT: Check the differences between consecutive terms, they are in AP.
Next time show your attempts, else you might not get any help here.
A: Just a few thoughts that might (might not) be helpful:
$$\begin{align}
0&\\
7 &= 0 + 7 + 0\cdot 2\\
16 &= 7 + 7 + 1\cdot 2\\
27 &= 16 + 7 + 2\cdot 2\\
40 &= 27 + 7 + 3\cdot 2
\end{align}
$$
A: This is a sequence defined by (n+6)n:
(0+6)0, (1+6)1, (2+6)2, (3+6)3, ..., (n+6)n
A: Here is a very simple way to solve such a problem: You notice that not the terms, but the increments are in arithmetic progression. I hope you also know that when the increment is linearly increasing, then by integration, the expression will be a quadratic equation. What you can do now is: Assume a quadratic equation of the form "ax^2 + bx + c = k". Here, 'x' is the variable corresponding to the nth term of the sequence, and 'k' is the value of the nth term; now simply put n=1, 2 and 3 to obtain 3 linear equations in 'a', 'b' and 'c', which can be solved for their values. And there you have your general quadratic expression. (Pardon the crude script, it's been a while since I used LATEX. Any editing would be appreciated.)
