 Hi, and welcome to the session. Let us discuss the following question. The question says that the Pivonichy sequence is defined by 1 is equal to a1 is equal to a2, and an is equal to an minus 1 plus an minus 2, n is greater than 2. Find an plus 1 upon an for n is equal to 1, 2, 3, 4, 5. Let's now begin with the solution. In the question we are given that a1 is equal to a2 is equal to a1, and an is equal to an minus 1 plus an minus 2, when n is greater than 2. Now, these are the two information given to us. And using these two information, we have to find the value of an plus 1 upon an. So let's first find the value of an plus 1 upon an for n is equal to 1. Now, for n is equal to 1, an plus 1 upon an is equal to a2 upon a1. And in the question, it is given that both a1 and a2 is equal to 1. So this is equal to 1. So for n is equal to 1, an plus 1 upon an is equal to 1. Now we will find the value of an plus 1 upon an for n is equal to 2. For n is equal to 2, an plus 1 upon an is equal to a3 upon a2, right? We know the value of a2, and we will find the value of a3 by using this second relation, since it is true for n greater than 2. Now, by substituting n as 3 in this relation, we get a3 is equal to a2 plus a1, both a1 and a2 is equal to 1. So this is equal to 2. So a3 by a2 is equal to 2 by 1, and this is equal to 2. Now we will find the value of an plus 1 upon an for n is equal to 3. For n is equal to 3, an plus 1 upon an is equal to a4 by a3. We have already found out the value of a3. Now we will find the value of a4. By substituting n as 4 in this relation, we get a4 is equal to a3 plus a2. a3 is equal to 2, and a2 is equal to 1. So this is equal to 3. So a4 by a3 is equal to 3 by 2. Now we will find the value of n plus 1 upon an for n is equal to 4. For n is equal to 4, an plus 1 upon an is equal to a5 by a4. We have already found out the value of a4. So let's now find the value of a5. We will replace n by 5 in this relation. Now this is equal to a4 plus a3. a4 is equal to 3, and a3 is equal to 2. So we have a5 as 5. So a5 by a4 is equal to 5 by 3. Now we will find the value of an plus 1 by an for n is equal to 5. For n is equal to 5, an plus 1 upon an is equal to a6 by a5. We already know the value of a5. So let's now find the value of a6. Now a6 is equal to a5 plus a4. a5 is equal to 5, and a4 is 3. So we have 5 plus 3, and this is equal to 8. Thus a6 by a5 is equal to 8 by 5. Hence the required value of an plus 1 by an for n is equal to 1 is 1. For n is equal to 2 is 2. For n is equal to 3 is 3 by 2. For n is equal to 4 is 5 by 3. And for n is equal to 5 is 8 by 5. This is our required answer. So this completes the session. Bye and take care.