 Hey welcome friends to another problem solving session on sequence and series. So let's take this problem up and try to solve this. In the given problem, it's given that an, the nth term of a sequence is given by this formula. We know that there are sequences whose nth term can be expressed in form of a formula. And let's say this is given here and it is asked to find out a7 and a8. It's very simple question. So in such cases we know what to do. We have to simply deploy the value of n into the formula and get it done or you can find out the value of the nth term. So let's find out a7 first. So a7 means n is equal to 7. So if n is equal to 7, an will be equal to 3 into 7 minus 2 divided by 4 into 7 plus 5. Just replace n by 7 and you will get a7. So this also should be replaced and this is a7. So what is this now? Simple arithmetic 21 minus 2 divided by 28 plus 5. And if you see this is nothing but 19 upon 33. So this is the a7 part. What is a8? So a8 simply will be n0, deploy n is equal to 8. So hence 3 into 8 minus 2 divided by 4 into 8 plus 5 and which is 24 minus 2 divided by 32 plus 5, which is 22 upon 37, correct? So this is very, very simple problem. You have to just find out the seventh and eighth term of the given sequence. So 19 upon 33 and 22 upon 37 are the two given a7 and a8. Now in this question it says that find the next five terms of the sequence given by this a1 is equal to 4 and an is equal to 4an minus 1 plus 3. So this is how the sequence has been defined. First term is given to be equal to 4 and then subsequent five terms, next five terms that is we have to find out a2, a3, a4, a5 and a6. These are the next five terms and if you know, this is the second type of relation. If you remember what we discussed in the previous session that nth term is a function of previous terms. It is this kind of a relationship, isn't it? So never mind we can, if the formula is given, we can easily find out a2, what will be a2? According to this formula, a2 will be a4, a1 plus 3, isn't it? So when it is n, this suffix is n minus 1. So if it is 2, it has to be 1, n minus 1, right? So hence this is the first term and a1 is, a1 is how much? 4. So 4 into 4 plus 3, that is 19, correct? This is a2. What about a3? a3 is 4 times a2, one previous term and then add 3 to it, so 4 into 19 plus 3, okay? So 4 into 19 is 76, 76 plus 3 is 79. I hope you are getting this, okay? Next is a4 and a4 is clearly 4 times a3 plus 3, so it is 4 times a3. So 4 into 79 plus 3, isn't it? And if you calculate it, it is nothing but 34, 9s or 36, carry 3. So 316 plus 3, so it is 319, very easy. So you are simply deploying what? Values of, so a5 is nothing but 4 into a4 plus 3, so simple arithmetic 4 into, what is a4? 319. Found out plus 3, so this is nothing but 376 plus 3, so hence it is 1279, very good. So what is a6, right? So you have to find out, find the next 5 terms, right? So next 5 terms, so a6 is 4 into a5 plus 3, which is 4 into 1279 plus 3. So let's multiply, so 5116 will be 4 into 1279, let's check it. So it is, yeah, plus 3. So hence it is 5119, right? So this is how you have to calculate, if the nth term formula is given expression or relationship is given, you can find out any nth term in that, okay?