input 100, 200, 300, 400 output 8.9, 18.5, 28.6, 39.5

Question

Need to find the rule for the following inputs and outputs.

Answer 1

Given series (green): 8.9, 18.5, 28.6, 39.5, 51.5, 64.9 (extrapolated series in red)

1st difference: 9.6, 10.1, 10.9, 12.0, 13.4

2nd difference: 0.5, 0.8, 1.1, 1.4

3rd difference 0.3 (assumed constant)

If the third difference is extrapolates, the 2nd difference increases by 0.3.

The 1st differences can then be predicted from the second differences to create the given series and its continuation.

This may be only one solution out of many solutions.