 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, 5 square plus 6 square plus 7 square plus goes on up to 20 square. So let's start with the solution and let the given series be denoted by s, so s is equal to 5 square plus 6 square plus 7 square plus goes on up to 20 square. Now let the k term of the series be denoted by a k. So a k is equal to plus 4 whole square thus the first term of the series can be written as 1 plus 4 whole square, second term can be written as 2 plus 4 whole square, third term can be written as 3 plus 4 whole square and the last term can be written as 16 plus 4 whole square. So k takes value from 1 up to and thus the k term will be k plus 4 whole square. So a k is equal to k square plus 8k plus 16 and now since we need to find the sum to n terms therefore taking summation on both the sides we have summation a k, k running from 1 to n is equal to summation k square k running from 1 to n plus 8 times summation k running from 1 to n k, 16 summation k running from 1 to n. So this is equal to summation k square k running from 1 to n is n into n plus 1 into 2n plus 1 upon 6 plus 8 into n into n plus 1 upon 2 plus 16 into n taking n upon 6 common. Here we have n square plus 3n plus 1 here taking 6 common from this term from the denominator we have 24 plus 1 and there we have plus 96. So this is further equal to n upon 6 into 2n square plus 3n plus 1 plus 24n plus 24 plus 96 which is further equal to n upon 6 into 2n square plus 27n plus 21. n is equal to 16 as the last value of k is 16. So we have to find the sum of 16 terms. So this is equal to summation a k, k running from 1 to 16 is equal to 16 upon 6 2 into 16 square plus 27 into 16 plus 121 this is equal to 2 x is 16 and 2 3s are 6 and here we have 2 into 16 into 16 plus 27 into 16 as 432 plus 121 which is further equal to 8 upon 3 into 512 plus 432 plus 121 which is equal to 8 upon 3 into 1065 or 8 upon 3 into 1065 which is equal to 8 into 355 which is equal to 2840 as the answer is the sum to n terms of the given series is 2840. So this complete specification take care and have a good day.