The Second method is the Iterative Method.

This method is excellent because by this method you can solve all the recurrence problems given in the Question on recurrence. 

Iterative Method - It means to expand the recurrence and express it as a summation of terms of n and initial condition. T(1) was the required time in the initial state. To transform the recursion, first, decompose T(n) into T(n/2) and then T(n/4) and then up to T(1).

You will get all the 25 answers in the Question on recurrence.

1. T(n) = T(n - 1) + 1       T(1) = 1


2. T(n) = T(n - 1) + n



3. T(n) = T(n - 1) + n^2



4. T(n) = T(n - 1) + log n



5. T(n) = T(n - 1) + 1/n



6. T(n) = T(n - 1) + √n



7. T(n) = 2T(n - 1) + n



8. T(n) = T(n - 1) + 2^n



9. T(n) = 2T(n - 1) + 2^n



10. T(n) = 2T(n - 1) + log n



11. T(n) = √5 T(n - 1) + n



12. T(n) = T(n/2) + n



13. T(n) = 2T(n/2) + 1



14. T(n) = 2T(n/2) + n



15. T(n) = 4T(n/2) + n^2



16. T(n) = 3T(n/2) + n



17. T(n) = 2T(n/3) + n



18. T(n) = 7T(n/2) + n^2



19. T(n) = (5/2)T(3n/2) + n



20. T(n) = 2T(n/4) + √n



21. T(n) = T(n/2) + log n



22. T(n) = T(n/2) + n log n



23. T(n) = 2T(n/2) + log n



24. T(n) = 2T(n/2) + n log n



25. T(n) = 2T(n/2) + n/ log n