Thread: Insertion Sort

Hi,
I have the following pseudo-code for Insertion Sort:

Code:

InsertionSort(Input: integer n, array A)
{
  for j = 2 to n {
    newnum  <-  A[j]
    i  <-  j-1
    while (i > 0 and newnum < A[i]) {
       A[i+1]  <-  A[i]
       i  <-  i-1
    }
    A[i+1]  <- newnum
  }
}

Suppose the number of iterations the while loop runs is r_A(j)=j-1 where r_A(j) denotes the number of elements in A whose value is greater than A[j] but precede it, i.e. the number of elements A[i] so that A[i]>A[j] but i<j for 1<=j<=n.
I would like to determine the time complexity using big theta and r_A(1), r_A(2)...r_A(n) only. I hence wrote the following:
T_IS(A) <= c1*n + c2[r_A(1)+r_A(2)+...+r_A(n)] which I believe to be correct (is it?), yet am not sure how to turn that into a big theta using r_A(1), r_A(2)...r_A(n) as required. Any advice? :-)