 Hi and welcome to the session. I am Shashi. Let us do one question. Question is, two APs have the same common difference. The difference between their hundred terms is hundred. What is the difference between their thousandth terms? First of all, let us understand the nth term of the AP, that is a n is equal to a plus n minus 1 multiplied by t, where a is the first term of AP and g is the common difference. This is the key idea to solve the given question. Let us now start with the solution. Two APs be a1, a2, a3 till a n and b1, b2, b3 till b n. Now, let the common difference of two APs be d. Now, nth term of the AP, a1, a2, a3 till a n is given by a n is equal to a1 plus n minus 1 multiplied by t. a1 is the first term of the AP and common difference we have assumed is equal to d. So, we can write nth term of the AP is equal to a1 plus n minus 1 multiplied by t. Now, we know hundred term of this AP would be equal to a1 plus hundred minus 1 multiplied by d. This implies hundred term is equal to a1 plus 99 b. Now, similarly the nth term of the AP, b1, b2, b3 till b n is given by b n is equal to b1 plus n minus 1 multiplied by t. Now, hundred term of this AP is equal to b100 is equal to b1 plus 100 minus 1 multiplied by d. This implies hundred term of this sequence is equal to b1 plus 99 d. Now, we are given that the difference between the hundred terms of two APs is 100. So, we can write a100 minus b100 is equal to 100. Now, substituting their corresponding values we can write a1 plus 99 d minus b1 plus 99 d is equal to 100. This implies a1 plus 99 d minus b1 minus 99 d is equal to 100. Now, minus 99 d and plus 99 d will get cancelled and we get a1 minus b1 is equal to 100. Now, the thousand term of AP a1 a2 a3 till a n is given by a1000 is equal to a1 plus 1000 minus 1 multiplied by d. Where a1 is the first term of the AP and d is the common difference. So, we get thousand term of the AP is equal to a1 plus 999 d. Now, similarly the thousand term of AP b1 b2 b3 till b n is given by b1000 is equal to b1 plus 1000 minus 1 multiplied by d. Where b1 is the first term of the AP and d is the common difference. Now, thousand term of this AP is equal to b1 plus 999 multiplied by d. Now, we have to find the difference between the thousand term of the two APs. So, therefore let x be the difference between the thousand terms of the two APs. So, we can write this implies a1 plus 999 d minus b1 plus 999 d is equal to x. Now, simplifying we get a1 plus 999 d minus b1 minus 999 d is equal to x. Now, 999 d and 999 d we will get it cancelled. So, we get a1 minus b1 is equal to x. Now, let us name this equation as 1. We had already obtained in equation 1 that a1 minus b1 is equal to 100. Now, substituting the value of a1 minus b1 is equal to 100 we get 100 is equal to x. So, therefore we get x is equal to 100. We know x was the difference between the thousand terms of the two APs. So, difference between thousand terms of the two APs is 100 as x is equal to 100. So, our required answer is 100. This completes the session. Hope you understood the session. Take care and goodbye.