Sequences puzzle

Pupils are given two fractions as the start of a sequence, and try to extend it.
Could be made easier or introduced using integers rather than fractions, maybe with some decimals and negatives in between. Works as either a ‘low floor high ceiling’ task, or as a way of revising different sequence types and also decimals, negatives and fractions. Particularly for the quadratic sequence, there’s scope to spend time looking at the algebra needed to find solutions.

Please let me know if you can think of any other ways to extend the task!