 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says find the sum to n terms of the series 3 into 8 plus 6 into 11 plus 9 into 14 plus so on. Let us now start with the solution and let the series be denoted by S. So S is equal to 3 into 8 plus 6 into 11 plus 9 into 14 plus the nth term of this series will be 3n into 3n plus 5 since the first term is 3 into 1 into 3 into 1 plus 5. Similarly the second term can be written as 3 into 2 into 3 into 2 plus 5. The third term of this series can be written as 3 into 3 into 3 into 3 into 3 plus 5 and so on. So let the kth term of the series be ak and ak will be equal to 3k into 3k plus 5. So ak is equal to 9k square plus 15k. Now we have to find the sum to n terms therefore taking summation on both the sides. We have summation ak k running from 1 to n the right hand side 9 times summation k square k running from 1 to n plus 15 times summation k k running from 1 to n. So this is for the equal to 9. Summation k square k running from 1 to n is n into n plus 1 into 2n plus 1 upon 6 plus 15 into n into n plus 1 upon 2. Now 3 3 is the 6, 9 and 3 2 is the 6. So here we have 3 upon 2 n into n plus 1 into 2n plus 1 plus 15 times n into n plus 1 upon 2. Now let us take 3 upon 2 into n into n plus 1 common. So here we have 2n plus 1 plus 5 which is equal to 3 upon 2 into n into n plus 1 into 2n plus 6. Now taking 2 common we have 3 upon 2 into 2 into n into n plus 1 into n plus 3. Now 2 answers are put 2 and we have 3n into n plus 1 into n plus 3. Thus sum to n terms of the given series is 3n into n plus 1 into n plus 3. So this completes the session. Take care and have a good day.