Hello, Soriku Strife!

Here's one approach to this problem (bear with me, it's quite long).Write a formula for the term of this quadratic sequence:

. . 7, 15, 27, 43, 63, . . .

We write a general quadratic function: .

. . and we must determine

We have three "unknowns", so we need three equations.

We'll use the first three terms of the sequence.

The first term is 7. .That is: .

. .

The second term is 15. .That is: .

. .

The third term is 27. .That is: .

. .

Subtract [4] from [5]: .

Substitute into [4]: .

Substitute into [1]: .

Therefore, the function is: .