Question: Assume we constructed a quicksort and the pivot value takes linear time. Find the recurrence for worst-case running time.

My answer:
T(n)= T(n-1) + T(1) + theta(n)

Worst case occurs when the subarrays are completely unbalanced.
There is 1 element in one subarray and (n-1) elements in the other subarray.
theta(n) because it takes running time n to find the pivot.

Am I doing this correctly?

Answer: 
you cannot observe, because according to my research T(N)= T(N-K)+T(K-1)+n
we cannot observe exact value until we have 
value of k,
T(n) = T(an/(a+b)) + T(bn/(a+b)) + n

Where a/(a+b) and b/(a+b) are fractions of array under consideration