 Hi and welcome to the session, let us discuss the following question, question says how many multiples of 4 lie between 10 and 250? Now let us start with the solution, we have to find number of multiples of 4 lying between 10 and 250, we know first multiple of 4 between 10 and 250 is 12, so we can write first multiple of 4 between 10 and 250 is 12 and we also know that last multiple of 4 between 10 and 250 is 248, so we can write last multiple of 4 between 10 and 250 is 248, now we get the series of multiples as 12, 16, 20, 24 till 248, clearly we can see this is an AP, now clearly we can see first term of AP is 12, so we can write first term of AP that is A n is equal to 12, now let us find out common difference, common difference is given by D this is equal to 20 minus 16, you know difference is equal to difference between two consecutive terms, now we get common difference is equal to 4, now nth term of AP that is A n is equal to A plus n minus 1 multiplied by D where A is the first term and D is the common difference, now let us assume that nth term of AP is 248, now we will substitute corresponding values of A n, D and A in this expression and we get 248 is equal to 12 plus n minus 1 multiplied by 4, now subtracting 12 from both the sides we get 248 minus 12 is equal to n minus 1 multiplied by 4, now simplifying further we get 236 is equal to n minus 1 multiplied by 4, now dividing both sides by 4 we get 236 upon 4 is equal to n minus 1, now we know 59 multiplied by 4 is equal to 236, so we get 59 is equal to n minus 1, now adding 1 on both the sides we get 60 is equal to n or we can write n is equal to 60, now we get total number of terms in the above AP is 60 or we can say there are 60 multiples of 4 between 10 and 250, so our required answer is 60, this completes the session hope you understood the session take care and have a nice day