Question

given the quadratic equation -2, 0, 3, 7 ...
Determine the expression of the nth term of this sequence

Answer 1

Which term of the sequence will be equal to 322?

Answer 2

the 1st differences are 2,3,4,...
so the nth term of the sum is
-2 + ∑(k=1,n-1) k+1 = -3+∑(k=0,n+1) k
Now we know that ∑(k=0,n+1) k = (n+1)(n+2)/2
so a_n = -3 + (n+1)(n+2)/2 = (n-1)(n+4)/2
which term is 322? n=24