 Hey, welcome friends once again to another problem solving session on arithmetic progression in this question We have a different variety of Problems or problem says that is 184 a term of the sequence three seven eleven dot dot dot So basically they're asking us to find out whether 184 Belongs to this sequence right so somewhere here 184 is there is this so is this so that's the question How to find out so we will start with the assumption that 184 is you know is a part of the sequence, so we'll start with this assumption, right? So let 184 184 belong to belong to The given AP Okay, this is an AP for sure because consecutive terms have the same difference That is for you can see that let 184 belong to the given AP right and It is at nth position Okay at nth position that means we are saying Tn is 184 Tn is 184 and what do I know about the you know sequence and this relationship between this You know nth term and the end so we know that Tn is equal to T1 plus n minus 1d Okay, in this case even clearly is 3 no doubts about it D will be equal to 7 minus 3 or 11 minus 7 whichever way which is 4 d is 4 So that means Tn is equal to 184 Must be equal to 3 plus n minus 1 times 4 Is it this is what if it if at all 184 is in the sequence it should obey this rule So hence there must be an n about n for it. So 184 minus 3 Divide by 4 is n minus 1. Isn't it that means n is equal to 181 by 4 Plus 1 that is 185 by 4 Correct, which is not an integer Yeah, not an integer Right, so but we know that if if 184 exists at nth position. So n must be an integer hence hence we conclude what 184 184 doesn't Doesn't does not that is belong to the given AP to the given AP right, so what is the learning guys So if someone is asking you to find out whether a particular term is part of a given AP or not Then try to show that it exists at an nth position and try to find out n from the given Conditions and the data if n happens to be an integer positive non-zero positive integer that is then That particular term definitely belongs to the AP otherwise not right. So this is how You can solve this problem