 Hello and welcome to all and in this session We are going to take up another problem on sequence and series and specifically about the middle term of an AP finding the middle term of an Arithmetic progression. So just a quick recap Whatever we have learned about the middle term and we know that if n that is the number of terms is odd then The there is only one middle term one middle term. This is just a recap One middle term and what is it? That is nothing but term number n plus 1 by 2, isn't it? This is the Middle term if n is odd and if n is even Okay, if n is even then there are two middle terms We all know that two middle terms and what all one is the t n by 2 and The second one is t n by 2 plus 1 right n by 2 plus 1 and n by 2 So hence what is the conclusion for finding out any middle term? We need to know whether the number of terms is even or odd So for let's first evaluate this arithmetic progression. So clearly t1 or a1 is 6 first term and Is it in AP? Yes looks like because the consecutive differences the difference between two consecutive terms is Constant and in this case D the common difference is how much common difference D is if you see 13 minus 6 Right, which is 7 Okay, so now let's find out the number of terms. So let's say number of terms is How much let's say number of terms is n? Okay, therefore 2 1 6 is the last term so 2 1 6 is the nth term in this case and first term is P1 plus n minus 1d that is what we have learned So 2 1 6 minus or is equal to 6 plus n minus 1 times 7 So this means n minus 1 times 7 it will be simply 2 1 6 minus 6 So n minus 1 happens to be 210 upon 7 which is 3 0 Disimplies n is equal to 31 Right, so n is 31. So what do we learn? We learn that n is 31 number of terms is right So which is an odd number odd number, correct. So hence middle term Middle term will be what? e of n plus 1 by 2 from this Relationship so this is t of 32 by 2 That is t 16 that is 16 term is the middle term. Let's find the 16th term So t 16 is nothing but e1 plus 16 minus 1 times d common difference Let's find out the value e1 is how much guys e1 was 6 check e1 was 6. Yes, and 16 minus 1 is 15 into d d is how much 7 So that means 6 plus 15 times 7 is 105 So the answer is 111 Okay, so 111 is the middle term of this AP