 Okay, friends, so let's solve another problem on finding the middle term of an AP. Okay, the question says find the middle term Slash S. So what does this mean? This is weird. Isn't it? What does this mean? This means that you don't know whether the number of terms is odd or even so depending on that It could be either one middle term or two middle terms if n is odd that is number of terms is Odd then there will be only one middle term if the number of terms is even then there will be two middle terms That is what we learned hence since it is hidden in the question So hence they have sin said terms last S So it could be one term or two terms hence of the AP. Okay. Now. What is the AP? It's given 7 13 19 25 241 first of all Well, you know, let's write the basics. So what is T1? T1 is 7 and what is the common difference is? 13 minus 7 that is 6 and Check whether the 6 is the common difference everywhere. Yes looks like yep So hence we have to find out the middle term for finding the middle terms or middle term or middle terms We need to find out the number of terms first in the AP because middle terms exist only in finite APs You cannot have middle terms in infinite APs So, let's find out n number of terms. Let it be n number of terms number of terms in the given AP in the Given AP Bn Okay, Bn let Number of terms terms in the given AP Bn then So last term will be the ns term in this case. What is last term guys 241? So 241 can be written as T1 plus n minus 1d indeed Right. So what is to 241 and T1 was how much 7 plus n minus 1 and D is how much 6? So that means n minus 1 will be simply 241 minus 7 upon 6, which is 234 upon 6, which is 6 3 times 18 and 39 Yep, so this is 39 n minus 1 is 39. So what is n here? So 39 plus 1 is 40, right? So n is 40. What is this? total number of terms total number of Terms where in the AP in the Given AP, right? Now what? if Number of terms are known. Now you can find out the middle term. So n is even so this happens to be an even number so if n is Even then There are two middle terms. There are two Middle terms and where are they? Which positions they are located? So they are located at T n upon 2 and T n upon 2 plus one of terms are the middle terms. So in this case T 40 by 2 and T 40 by 2 Plus one that is T 20 and T 21 are the Middle terms, right? No, so 20th and 21st term. So let's find out what will be T 20 T 20 is not the cricket match T 20s term 20 here T 20 is first term What is first term first term given was 7 you can check first term was 7. Yes and 20 minus 1 times 6 Right, which is 7 into 19 times 6 Correct, which happens to be 121 Right now T 21 will be 7 plus 21 minus 1 times 6 Which will be equal to 7 into 20 into 6 that is 1 27 right You could have found out T 21 simply by this as well T 21 is T 20 plus the common difference Right T 20 was 121 plus D was 6. So hence it is 127 whichever way, right? Either this way or that way, right? You can figure out and hence we got two middle terms 121 and 127 Are the middle terms of this AP?