Nth term pls help

[sacred sandal]

use the binomial theorem

[royal skiff]

plug in 3 known terms then solve for the coefficients of the general term

or the term is obvious in which you can just write it down after a bit of thought

[wooden glacier]

What is a "quadratic sequence"?

[royal skiff]

sequence where the nth term is given by a quadratic

[wooden glacier]

Right.

[verbal yacht]

but i learnt it like this:

0 , 3 , 6 , 9 , 12 , ....

tn = t1 + ( n - 1 ) d
= 0 + ( n - 1) 3
= 0 + 3n - 3
= 3n -3

[verbal yacht]

what is a binomial theorem

[wooden glacier]

That's not a quadratic sequence.

[verbal yacht]

ik but i don't know how to find the nth term of the quadratic sequence

i only know how to do it the normal way

[verbal yacht]

pls help

[wooden glacier]

Okay, look. What's the sequence?

[verbal yacht]

0 , 3 , 8 , 15 , 24 , ...

[spare remnant]

@verbal yacht

In a quadratic equation what is the greatest power that can be and has to be present?

[royal skiff]

Note that the sequence is 1-1,4-1,9-1,16-1,25-1

[wooden glacier]

So the sequence goes: 0 1 2 3 4 0: 0, 3, 8, 15, 24... 1: 3, 5, 7, 9... 2: 2, 2, 2... 3: 0, 0...
Where the row number indicates the nth difference, and the column number indicates the nth term in that sequence. The nth term of the 0th difference is given by sum(i = 0, inf) d^i(0) * iCn, where d^i(0) indicates the 0th term of the ith difference.

In this specific case, it would be 0 * nC0 + 3 * nC1 + 2 * nC2 + 0 * ... = 3 * nC1 + 2 * nC2 = 3n + 2 * n(n - 1)/2 = 3n + n(n - 1) = n^2 + 3n - n = n^2 + 2n