What's the process if the input numbers are 1,2,3,4,5 and the output numbers are 2,5,10,17,26

Answer 1

since the differences are 3,5,7,9
and the 2nd differences are all 2, you expect a quadratic.

A little thought shows that

y = x^2+1

Answer 2

if the input number is 1 2 3 4 5 what will be the output number