a1 = 600
d = 3.1

 <-- the formula for the nth term of an A.P.

 <-- substituted for a1 and d

  <-- moved the 3.1 to the left of (n-1)

 <-- distributed

 <-- combined like terms

Edwin

In the given context, there is no such thing (such conception) as weekly height of the tree.


There is "the height of the tree at the moment when you measure it" - for example, at the beginning of each week.


Under this conception, the height of the tree at the beginning of n-th week is


     h(n) = (600-3.1) + 3.1*n  centimeters = 596.9 + 3.1*n centimeters, n = 1, 2, 3, 4 . . .     (1)


You start from 600 cm at the time moment t= 0. 
It corresponds to the beginning of the first week: n= 1,  h(1) = 600 cm.
And then you have h(n) according to the formula (1), at the beginning of each next (n-th) week.