Which one of these formulas describes the following sequence?

1,5,12,22,35

We can find a formula for nth term of the given sequence as follows:

1, 5, 12, 22, 35

The 1st differences between terms:

4, 7, 10, 13

The 2nd differences :

3, 3, 3

Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: , where c is a constant. The coefficients a, b, and the constant c can be found.

We can form the following 3 equations with 3 unknowns a, b, c:

Solving for a, b, c, we get:

a = 3/2, b = -1/2, c = 0

Therefore, the nth term of the given sequence is:

2

step-by-step explanation:

vvvvv