Hello, Trin769!

Is there an easier way to work out a number sequence which isn't linear?

If we know that the formula is a *quadratic*, there is a sneaky way,

. . but you may need some background.

We begin with a basic quadratic function: .

This generates the Triangular Numbers: 1, 3, 6, 10, 15, . . .

And it should be obvious why they are called "triangular." Code:

o
o o o
o o o o o o
o o o o o o o o o o
1 3 6 10

So we have the formula: .

. . and we will *modify* it to fit the given sequence: 1, 2, 4, 7, 11, 16, 22, . . .

For the first few values, compare our sequence to the triangular numbers

. .

The values of do not match those of

. . Some adjustments are necessary . . . let's examine them.

. .

We see that we must subtract a number one less than

. . Hence: .

And we have: .

. . Therefore: .