 Hi and welcome to the session, I am Asha and I am going to help you with the following question which says, if the sum of n terms of an AP is 3n square plus 5n and its emit term is 164, find the value of m. Let us now begin with the solution and we are given that sum of n terms which is denoted by Sn is equal to 3n square plus 5n. Let the AP be a1, a2, a3, a4 and so on up to an. Let us take n is equal to 1 and S1 which is equal to a1 will be equal to 3 and replaced by 1 gives 8. Now, let n is equal to 2, so the sum of first two terms that is a1 plus a2 will be equal to 3 into 2 whole square plus 5 into 2 which is equal to 3 into 4 plus 10 which is equal to 22. Now, to find the a2n term we will subtract the sum of first two terms minus S1, so this is equal to 22 minus 8 which gives us 14. So, the second term of the sequence is 14. Now, let us find the common difference d which is a2 minus a1, so 14 minus 8 is equal to 6. Therefore, we have d is equal to 6. Now, we have to find the mth term which is equal to am will be a1 plus first term plus m minus 1 into d. Now, we are given that the mth term is 164 and we have to find the value of m. So, this is equal to a1 is 8 plus m minus 1 into 6. So, this is further equal to 164 minus 8 is equal to m minus 1 into 6 which further implies that 156 is equal to m minus 1 into 6 or m minus 1 is equal to 156 upon 6 which implies m minus 1 is equal to 26 or m is equal to 27. Thus, the value of m is 27. So, this completes the session. Take care and bye.