 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that using inductive reasoning, complete the following conductor, the number of sites of a polygon that has n vertices is We know that in inductive reasoning we derive the conclusion after performing investigations, observing similarities and patterns and then making generalizations. With this key idea we shall move on to the solution. In this question we have to complete the conductor that is the number of sites of a polygon that has n vertices is Now let us start with drawing a few polygons and we know that minimum 3 vertices are required to draw a polygon. So let us take 3 points and then join these points we get a triangle which has 3 sites so a polygon with 3 vertices has 3 sites. Now let us take 4 points now we join these points we see that joining these points gives us a polygon having 4 sites so we get a polygon with 4 vertices has 4 sites. Now let us take 5 points and we join these points we see by joining these points we get a polygon having 5 sites so we can say that a polygon with 5 vertices has 5 sites. Now let us take 6 points now we join these points we see joining these points gives us a polygon having 6 sites so a polygon with 6 vertices has 6 sites so we have got the following pattern. Now looking at all these cases we can find the number of sites of a polygon having 7 vertices without actually drawing it and it is equal to 7 so we say that a polygon with 7 vertices has 7 sites. Thus we can draw the conclusion using inductive reasoning that is a polygon having n vertices will have n sites thus our conjecture is the number of sites of a polygon that has n vertices is n. This is the required answer. This completes our session hope you enjoyed this session.