What happens in In arithmetic growth In arithmetic cell division In arithmetic growth?
In arithmetic growth, after mitotic division only one cell continues to divide and the others differentiate and mature. For eg - root elongating at a constant rate.

Mathematically it is expressed as. 

begin mathsize 20px style bold L subscript bold t bold space bold equals bold space bold L subscript bold o bold space end subscript bold space bold plus bold space bold rt end style

L= Length at time 't'
Lo Length at time 'zero'
r = Growth rate