Question

Find a recursive formula for the sequence:

3, -5, 11, -21

Answer 1

The correct option is the last:

$a_n = -2a_{n-1}+1$

In fact, every term in the sequence is one more than twice the opposite of the previous one:

We start with 3. Twice its opposite is -6. Plus one, we get -5.

We start with -5. Twice its opposite is 10. Plus one, we get 11.

We start with 11. Twice its opposite is -22. Plus one, we get -21.