How do you find the Nth term given this set of numbers?

-1, -2, -7, -16, -29, -46


I know that the difference between each difference (-1, -5, -9, -13, -17) is 4 each time, so how do I get the equation for the Nth term?





I know there must be a formula for it, but what is it?How do you find the Nth term given this set of numbers?
Let a(0) = -1, a(1) = -2, a(2) = -7, ...





The differences d(n) = a(n) - a(n- 1) are given by


d(n) = 3 - 4n, for n = 1, 2, 3,...





So


a(1) - a(0) = 3 - 4


a(2) - a(1) = 3 - 2*4


a(3) - a(2) = 3 - 3*4


...


a(n) - a(n-1) = 3 - n*4





By taking sums we get


a(n) - a(0)


= 3+3+...+ 3 - 4 - 2*4 - 3*4 -... - n*4


= n*3 - 4(1 + 2 + 3 +...+ n)


= 3n -4n(n+1)/2


= 3n - 2n(n+1)


Since a(0) = -1, we get


a(n) = -1 + 3n -2n(n+1)