 Okay, friend. So in this session, we are going to take up some questions on arithmetic progression and its general term So the question says show that the sequence 9 12 15 18 is an AP and find its 16th term and the general term, right? So how to solve this and how to show that any Sequence is an AP so solution will be something like that. So for an AP for an AP What do we know? T2 minus T1 should be equal to T3 minus T2 should be equal to T4 minus T3 and so on and so forth. This must be equal to the common difference D Okay, so let's find out T2. So if T2 if you see T2 T2 is equal to 12 right and T1 is equal to 9 So T2 minus T1 is 12 minus 9 is 3 Right, let's check if this common difference is same T3 is 15 T2 is 12. So hence T3 minus T2 is equal to 15 minus 12 this is also equal to 3 Okay, similarly T4 is 18 and T3 is given to be equal to 15 So hence T4 minus T3 is equal to 18 minus 15 is equal to 3 So you can show at least three Terms, you know or you can you know if you are clear that there is no No mismatch or no, you know anomaly. So all all these are Same difference right if there is anything. Let's say for example here It would be 19 then you can show that clearly. This is not an AP because 19 minus 18 is not 3 Okay, so clearly it is an AP. So what is the first term first term T1 is Given to be equal to 9 and what is D? D is 3 So first, let's find out the general term. So Tn general term will be first term We have learned this formula plus n minus 1 times D that is 3 Okay, so this is our formula for general term This is the formula for General term, isn't it? So we can write the values. So for example T1 is 9 Plus n minus 1 3 So if you solve this, this is 3 plus 3n minus 3 So hence it becomes 3n plus 6 Okay, so this is the general term. So what do we learn Tn is 3 times n plus 6. So we got a formula for the general term. So hence you have to find out T16 16th term will be T3 into 16 plus 6. So it is nothing but 48 plus 6 is 54