Consider the sequence below : -2,1,6,13,22,... What explicit expression can be used to find the nth term of this sequence ?

Question

Having trouble with this one

Answer 1

That's because it is neither arithmetic nor geometric. However, while the differences are not constant, the follow a predictable pattern: add 3, add 5, add 7, etc. The recursive formula is easier to get ...

t₁ = -2 , t_n+1 = t_n + (2n + 1).

For the explicit formula, note that the sequence has constant 2nd differences, characteristic of a quadratic:

t_n = n² - 3

Answer 2

F(n) = f(n-1)+d(n), f(1)=--2

D(n)= 2n-1