Find General Form of Series - System of Equations with Elimination Method

Find the general form of a series of perfect squares. By using a system of equations with the elimination method to solve for the coefficients, then solve for n, finally, check our work with the delta difference operation.

Double checked our work from Wolfram.

If you're wondering where the expressions came from to solve for coefficients of a cubic polynomial check a previous video:

https://rumble.com/v5fxgjx-delta-difference-operation-find-formula-for-a-sequence-then-solve-for-n.html

6a, 12a+2b, 7a+3b+c, a+b+c+d, upon solving for (a) then plug into next expression to solve for (b), continue the procedure until (d) is solved.

Sources:
Kahn Academy YT Channel - Sal

Gelfand, Gerver, Kirillov, Konstantinov and Kushnirenko - Sequences: 1969, problem 26