What is the equation for this sequence of numbers

First x, then y;
x y
1 1
2 3
3 6
4 10
5 15
6 21
7 28
8 36
9 45
10 55
11 66
12 78

There is no single equation for any list of numbers like that. There are an infinite number of equations that would fit. For example:

y = 0.5x^2 + 0.5x

But this also works:
y = -25 +78.080265x -100.31175x^2 +73.800112x^3 -34.300868x^4 + 10.755191x^5 -2.3481253x^6 +0.36151413x^7 -0.039115892x^8 +0.0029107418x^9 -0.00014180537x^10 +0.0000040709676x^11
-0.000000052191892x^12

The problem doesn't say to find a /simple/ equation, does it?

Have a good look at the numbers. There is addition invovled and it is not numbers in the x column added to other numbers in the x column.

Each instance of a row can be called a specific number. The first instance of x can be called x(1). The second instance of x can be called x(2). So if you were to take the fourth instance of x and add it to the eighth instance of x you could write the equation as

x(4) + x(8) = answer

Now, in your math text they probably used notation a little different than this. I do not know how to use superscripts and subscripts.

Hint: Figure out how to let your teacher know how to show you want to add the number from one instance to number of another instance.