 Hi and welcome to the session. I am Arsha and I am going to help you with the following version that says, find the sum of the following series to n terms. First is 5 plus 5 5 plus 5 5 5 plus 1 up to n terms. So let us start with the solution and let S n denote the sum of 5 plus 5 5 plus 5 5 5 plus so on to n terms. Now taking 5 common we have 1 plus 11 plus 111 plus so on to n terms. Now multiplying both the numerator and denominator by 9. So we have 5 upon 9 and multiplying 9 with the bracket. So multiplying 9 with each term of the bracket we have 9 plus 99 plus 99 and 99 plus so on to n terms and now this can further be written as 5 upon 9 10 to 9 can be written as 10 minus 1. 99 can be written as 100 minus 1 plus plus 999 can be written as 1000 minus 1 plus so on to n terms into 10 plus 100 plus 1000 plus to n terms minus 5 upon 9 into 1 plus 1 plus 1 n terms. So this is further equal to 5 upon 9 into 10 plus 10 square plus up to n terms minus 5 upon 9 into n. Now as we can see this is a GP series and for a GP series A AR AR square to n terms sum of these n terms is given by A where A is the first term into r raised to the power n minus 1 upon r minus 1 where r is the common ratio. So apply this formula on this GP series we have 5 upon 9 into A is 10 r is 10 square upon 10 again 10 so 10 raised to the power n minus 1 upon 10 minus 1 minus 5 upon 9 into n which is equally equal to 5 upon 9 into 1 upon 9 into 10 into 10 raised to the power n minus 1 minus 5 upon 9 into n. This can further be written as 50 upon 80 minus 10 raised to the power n minus 1 minus 5n upon 9. That is the answer is the sum of the given series is 50 upon 80 minus 10 raised to the power n minus 1 minus 5n upon 9. This completes the session. Take care and have a good day.