Find the sum of the first 125 terms of the sequence 1,2,1,3,2,1,4,3,2,1,5,4,3,2... Please give me explaination as I already have solution and give the best possible solution which is quick and easy to grasp. I got the solution though but with brute force which is quite cumbersome and time consuming and certainly not feasible.

series is in the form of 1,2    1,3,2   1,4,3,2    1,5,4,3,2 as you can see series is will go on like this till the 125th term by then you can say that when 1,2 there is no. of 1=1 when 1,3,2 the no. of 1's are=2 when 1,4,3,2 the  no.of 1's are=3 to simplify we can say that no of 1's =next term near to 1 -1 same goes for 2 and 3 and so on